Serre, JeanPierre 1926
Overview
Works:  322 works in 1,602 publications in 9 languages and 18,533 library holdings 

Genres:  Conference papers and proceedings Records and correspondence Sources History 
Roles:  Author, Editor, Collector, Other, Author of introduction, Interviewee, 956, Opponent, Honoree, Commentator 
Classifications:  QA171, 512.2 
Publication Timeline
.
Most widely held works about
JeanPierre Serre
 Correspondance SerreTate by JeanPierre Serre( Book )
 Chow's Theorem by Yohannes D Asega( )
 Feit, Walter, papers by Walter Feit( )
Most widely held works by
JeanPierre Serre
Linear representations of finite groups by
JeanPierre Serre(
Book
)
99 editions published between 1966 and 2014 in 7 languages and held by 1,497 WorldCat member libraries worldwide
This book consists of three parts, rather different in level and purpose. The first part was originally written for quantum chemists. It describes the correspondence, due to Frobenius, between linear representations and characters. This is a fundamental result of constant use in mathematics as well as in quantum chemistry or physics. The examples in this part are chosen from those useful to chemists. The second part is a course given in 1966 to secondyear students of l'Ecole Normale. It completes in a certain sense the first part. The third part is an introduction to Brauer Theory. Several Applications to the Artin representation are given
99 editions published between 1966 and 2014 in 7 languages and held by 1,497 WorldCat member libraries worldwide
This book consists of three parts, rather different in level and purpose. The first part was originally written for quantum chemists. It describes the correspondence, due to Frobenius, between linear representations and characters. This is a fundamental result of constant use in mathematics as well as in quantum chemistry or physics. The examples in this part are chosen from those useful to chemists. The second part is a course given in 1966 to secondyear students of l'Ecole Normale. It completes in a certain sense the first part. The third part is an introduction to Brauer Theory. Several Applications to the Artin representation are given
A course in arithmetic by
JeanPierre Serre(
Book
)
71 editions published between 1970 and 2013 in 5 languages and held by 1,227 WorldCat member libraries worldwide
This book is divided into two parts. The first one is purely algebraic. Its objective is the classification of quadratic forms over the field of rational numbers (HasseMinkowski theorem). It is achieved in Chapter IV. The first three chapters contain some preliminaries: quadratic reciprocity law, padic fields, Hilbert symbols. Chapter V applies the preceding results to integral quadratic forms of discriminant ± I. These forms occur in various questions: modular functions, differential topology, finite groups. The second part (Chapters VI and VII) uses "analytic" methods (holomor phic functions). Chapter VI gives the proof of the "theorem on arithmetic progressions" due to Dirichlet; this theorem is used at a critical point in the first part (Chapter Ill, no. 2.2). Chapter VII deals with modular forms, and in particular, with theta functions. Some of the quadratic forms of Chapter V reappear here. The two parts correspond to lectures given in 1962 and 1964 to second year students at the Ecole Normale Superieure. A redaction of these lectures in the form of duplicated notes, was made by J.J. Sansuc (Chapters IIV) and J.P. Ramis and G. Ruget (Chapters VIVII). They were very useful to me; I extend here my gratitude to their authors
71 editions published between 1970 and 2013 in 5 languages and held by 1,227 WorldCat member libraries worldwide
This book is divided into two parts. The first one is purely algebraic. Its objective is the classification of quadratic forms over the field of rational numbers (HasseMinkowski theorem). It is achieved in Chapter IV. The first three chapters contain some preliminaries: quadratic reciprocity law, padic fields, Hilbert symbols. Chapter V applies the preceding results to integral quadratic forms of discriminant ± I. These forms occur in various questions: modular functions, differential topology, finite groups. The second part (Chapters VI and VII) uses "analytic" methods (holomor phic functions). Chapter VI gives the proof of the "theorem on arithmetic progressions" due to Dirichlet; this theorem is used at a critical point in the first part (Chapter Ill, no. 2.2). Chapter VII deals with modular forms, and in particular, with theta functions. Some of the quadratic forms of Chapter V reappear here. The two parts correspond to lectures given in 1962 and 1964 to second year students at the Ecole Normale Superieure. A redaction of these lectures in the form of duplicated notes, was made by J.J. Sansuc (Chapters IIV) and J.P. Ramis and G. Ruget (Chapters VIVII). They were very useful to me; I extend here my gratitude to their authors
Local fields by
JeanPierre Serre(
Book
)
63 editions published between 1962 and 2013 in 4 languages and held by 1,102 WorldCat member libraries worldwide
The goal of this book is to present local class field theory from the cohomo logical point of view, following the method inaugurated by Hochschild and developed by ArtinTate. This theory is about extensionsprimarily abelianof "local" (i.e., complete for a discrete valuation) fields with finite residue field. For example, such fields are obtained by completing an algebraic number field; that is one of the aspects of "localisation". The chapters are grouped in "parts". There are three preliminary parts: the first two on the general theory of local fields, the third on group coho mology. Local class field theory, strictly speaking, does not appear until the fourth part. Here is a more precise outline of the contents of these four parts: The first contains basic definitions and results on discrete valuation rings, Dedekind domains (which are their "globalisation") and the completion process. The prerequisite for this part is a knowledge of elementary notions of algebra and topology, which may be found for instance in Bourbaki. The second part is concerned with ramification phenomena (different, discriminant, ramification groups, Artin representation). Just as in the first part, no assumptions are made here about the residue fields. It is in this setting that the "norm" map is studied; I have expressed the results in terms of "additive polynomials" and of "multiplicative polynomials", since using the language of algebraic geometry would have led me too far astray
63 editions published between 1962 and 2013 in 4 languages and held by 1,102 WorldCat member libraries worldwide
The goal of this book is to present local class field theory from the cohomo logical point of view, following the method inaugurated by Hochschild and developed by ArtinTate. This theory is about extensionsprimarily abelianof "local" (i.e., complete for a discrete valuation) fields with finite residue field. For example, such fields are obtained by completing an algebraic number field; that is one of the aspects of "localisation". The chapters are grouped in "parts". There are three preliminary parts: the first two on the general theory of local fields, the third on group coho mology. Local class field theory, strictly speaking, does not appear until the fourth part. Here is a more precise outline of the contents of these four parts: The first contains basic definitions and results on discrete valuation rings, Dedekind domains (which are their "globalisation") and the completion process. The prerequisite for this part is a knowledge of elementary notions of algebra and topology, which may be found for instance in Bourbaki. The second part is concerned with ramification phenomena (different, discriminant, ramification groups, Artin representation). Just as in the first part, no assumptions are made here about the residue fields. It is in this setting that the "norm" map is studied; I have expressed the results in terms of "additive polynomials" and of "multiplicative polynomials", since using the language of algebraic geometry would have led me too far astray
Algèbres de Lie semisimples complexes by
JeanPierre Serre(
Book
)
52 editions published between 1966 and 2017 in 3 languages and held by 1,099 WorldCat member libraries worldwide
These short notes, already wellknown in their original French edition, give the basic theory of semisimple Lie algebras over the complex numbers, including classification theorem. The author begins with a summary of the general properties of nilpotent, solvable, and semisimple Lie algebras. Subsequent chapters introduce Cartan subalgebras, root systems, and linear representations. The last chapter discusses the connection between Lie algebras, complex groups and compact groups; it is intended to guide the reader towards further study
52 editions published between 1966 and 2017 in 3 languages and held by 1,099 WorldCat member libraries worldwide
These short notes, already wellknown in their original French edition, give the basic theory of semisimple Lie algebras over the complex numbers, including classification theorem. The author begins with a summary of the general properties of nilpotent, solvable, and semisimple Lie algebras. Subsequent chapters introduce Cartan subalgebras, root systems, and linear representations. The last chapter discusses the connection between Lie algebras, complex groups and compact groups; it is intended to guide the reader towards further study
Lie algebras and Lie groups; 1964 lectures given at Harvard University by
JeanPierre Serre(
Book
)
49 editions published between 1965 and 2006 in 3 languages and held by 1,097 WorldCat member libraries worldwide
This book reproduces JP. Serre's 1964 Harvard lectures. The aim is to introduce the reader to the "Lie dictionary": Lie algebras and Lie groups. Special features of the presentation are its emphasis on formal groups (in the Lie group part) and the use of analytic manifolds on padic fields. Some knowledge of algebra and calculus is required of the reader, but the text is easily accessible to graduate students, and to mathematicians at large
49 editions published between 1965 and 2006 in 3 languages and held by 1,097 WorldCat member libraries worldwide
This book reproduces JP. Serre's 1964 Harvard lectures. The aim is to introduce the reader to the "Lie dictionary": Lie algebras and Lie groups. Special features of the presentation are its emphasis on formal groups (in the Lie group part) and the use of analytic manifolds on padic fields. Some knowledge of algebra and calculus is required of the reader, but the text is easily accessible to graduate students, and to mathematicians at large
Galois cohomology by
JeanPierre Serre(
Book
)
68 editions published between 1963 and 2013 in 4 languages and held by 874 WorldCat member libraries worldwide
Annotation
68 editions published between 1963 and 2013 in 4 languages and held by 874 WorldCat member libraries worldwide
Annotation
Algèbre locale, multiplicités; cours au Collège de France, 19571958 by
JeanPierre Serre(
Book
)
68 editions published between 1965 and 2002 in 5 languages and held by 786 WorldCat member libraries worldwide
This edition reproduces the 2nd corrected printing of the 3rd edition of the now classic notes by Professor Serre, long established as one of the standard introductory texts on local algebra. Referring for background notions to Bourbaki's "Commutative Algebra" (English edition SpringerVerlag 1988), the book focusses on the various dimension theories and theorems on mulitplicities of intersections with the CartanEilenberg functor Tor as the central concept. The main results are the decomposition theorems, theorems of CohenSeidenberg, the normalisation of rings of polynomials, dimension (in the sense of Krull) and characteristic polynomials (in the sense of HilbertSamuel)
68 editions published between 1965 and 2002 in 5 languages and held by 786 WorldCat member libraries worldwide
This edition reproduces the 2nd corrected printing of the 3rd edition of the now classic notes by Professor Serre, long established as one of the standard introductory texts on local algebra. Referring for background notions to Bourbaki's "Commutative Algebra" (English edition SpringerVerlag 1988), the book focusses on the various dimension theories and theorems on mulitplicities of intersections with the CartanEilenberg functor Tor as the central concept. The main results are the decomposition theorems, theorems of CohenSeidenberg, the normalisation of rings of polynomials, dimension (in the sense of Krull) and characteristic polynomials (in the sense of HilbertSamuel)
Algebraic groups and class fields : translation of the French edition by
JeanPierre Serre(
Book
)
45 editions published between 1959 and 2012 in 4 languages and held by 709 WorldCat member libraries worldwide
Of the Main Results  Algebraic Curves  Maps From a Curve to a Commutative Group  Singular Algebraic Curves  Generalized Jacobians  Class Field Theory  Group Extension and Cohomology  Bibliography  Supplementary Bibliography  Index
45 editions published between 1959 and 2012 in 4 languages and held by 709 WorldCat member libraries worldwide
Of the Main Results  Algebraic Curves  Maps From a Curve to a Commutative Group  Singular Algebraic Curves  Generalized Jacobians  Class Field Theory  Group Extension and Cohomology  Bibliography  Supplementary Bibliography  Index
Cohomologie galoisienne, cours au Collège de France, 19621963 by
JeanPierre Serre(
Book
)
52 editions published between 1964 and 1986 in 4 languages and held by 708 WorldCat member libraries worldwide
52 editions published between 1964 and 1986 in 4 languages and held by 708 WorldCat member libraries worldwide
Trees by
JeanPierre Serre(
Book
)
30 editions published between 1980 and 2013 in English and Undetermined and held by 670 WorldCat member libraries worldwide
The present book is an English translation of "Arbres, Amalgames, SL(2)", published in 1977 by JP. Serre, and written with the collaboration of H. Bass. The first chapter describes the "arboreal dictionary" between graphs of groups and group actions on trees. The second chapter gives applications to the BruhatTits tree of SL(2) over a local field
30 editions published between 1980 and 2013 in English and Undetermined and held by 670 WorldCat member libraries worldwide
The present book is an English translation of "Arbres, Amalgames, SL(2)", published in 1977 by JP. Serre, and written with the collaboration of H. Bass. The first chapter describes the "arboreal dictionary" between graphs of groups and group actions on trees. The second chapter gives applications to the BruhatTits tree of SL(2) over a local field
Modular functions of one variable V : proceedings, international conference, University of Bonn, Sonderforschungsbereich
Theoretische Mathematik, July 214, 1976 by International Conference on Modular Functions of One Variable V(
Book
)
27 editions published in 1977 in 3 languages and held by 480 WorldCat member libraries worldwide
27 editions published in 1977 in 3 languages and held by 480 WorldCat member libraries worldwide
Lectures on the MordellWeil theorem by
JeanPierre Serre(
Book
)
19 editions published between 1989 and 1997 in English and held by 385 WorldCat member libraries worldwide
19 editions published between 1989 and 1997 in English and held by 385 WorldCat member libraries worldwide
Local algebra by
JeanPierre Serre(
Book
)
16 editions published between 2000 and 2011 in English and held by 377 WorldCat member libraries worldwide
This is an English translation of the now classic "Algèbre Locale  Multiplicités" originally published by Springer as LNM 11, in several editions since 1965. It gives a short account of the main theorems of commutative algebra, with emphasis on modules, homological methods and intersection multiplicities ("Torformula"). Many modifications to the original French text have been made by the author for this English edition: they make the text easier to read, without changing its intended informal character
16 editions published between 2000 and 2011 in English and held by 377 WorldCat member libraries worldwide
This is an English translation of the now classic "Algèbre Locale  Multiplicités" originally published by Springer as LNM 11, in several editions since 1965. It gives a short account of the main theorems of commutative algebra, with emphasis on modules, homological methods and intersection multiplicities ("Torformula"). Many modifications to the original French text have been made by the author for this English edition: they make the text easier to read, without changing its intended informal character
Topics in Galois theory by
JeanPierre Serre(
Book
)
12 editions published between 1992 and 2008 in English and held by 362 WorldCat member libraries worldwide
This book is based on a course given by the author at Harvard University in the fall semester of 1988. The course focused on the inverse problem of Galois Theory: the construction of field extensions having a given finite group as Galois group. In the first part of the book, classical methods and results, such as the Scholz and Reichardt construction for pgroups, p!= 2, as well as Hilbert's irreducibility theorem and the large sieve inequality, are presented. The second half is devoted to rationality and rigidity criteria and their application in realizing certain groups as Galois groups of
12 editions published between 1992 and 2008 in English and held by 362 WorldCat member libraries worldwide
This book is based on a course given by the author at Harvard University in the fall semester of 1988. The course focused on the inverse problem of Galois Theory: the construction of field extensions having a given finite group as Galois group. In the first part of the book, classical methods and results, such as the Scholz and Reichardt construction for pgroups, p!= 2, as well as Hilbert's irreducibility theorem and the large sieve inequality, are presented. The second half is devoted to rationality and rigidity criteria and their application in realizing certain groups as Galois groups of
Galois groups over Q : proceedings of a workshop held March 2327, 1987 by
Y Ihara(
Book
)
14 editions published in 1989 in English and Multiple languages and held by 359 WorldCat member libraries worldwide
This volume is being published in connection with a March, 1987 workshop on Galois groups over Q and related topics, held at the Mathematical Sciences Research Institute in Berkeley. The organizing committee for the workshop consisted of Kenneth Ribet (chairman), Yasutaka Ihara, and JeanPierre Serre. The volume contains key original papers by experts in the field, and treats a variety of questions in arithmetical algebraic geometry. A number of the contributions discuss Galois actions on fundamental groups, and associated topics: these include Fermat curves, Gauss sums, cyclotomic units, and motivic questions. Other themes which reoccur include semistable reduction of algebraic varieties, deformations of Galois representations, and connections between Galois representations and modular forms. The authors contributing to the volume are: G.W. Anderson, D. Blasius, D. Ramakrishnan, P. Deligne, Y. Ihara, U. Jannsen, B.H. Matzat, B. Maszur, and K. Wingberg. The contributions are of exceptionally high quality, and this book will have permanent value. The volume will be of great interest to students and established workers in many areas of algebraic number theory and algebraic geometry
14 editions published in 1989 in English and Multiple languages and held by 359 WorldCat member libraries worldwide
This volume is being published in connection with a March, 1987 workshop on Galois groups over Q and related topics, held at the Mathematical Sciences Research Institute in Berkeley. The organizing committee for the workshop consisted of Kenneth Ribet (chairman), Yasutaka Ihara, and JeanPierre Serre. The volume contains key original papers by experts in the field, and treats a variety of questions in arithmetical algebraic geometry. A number of the contributions discuss Galois actions on fundamental groups, and associated topics: these include Fermat curves, Gauss sums, cyclotomic units, and motivic questions. Other themes which reoccur include semistable reduction of algebraic varieties, deformations of Galois representations, and connections between Galois representations and modular forms. The authors contributing to the volume are: G.W. Anderson, D. Blasius, D. Ramakrishnan, P. Deligne, Y. Ihara, U. Jannsen, B.H. Matzat, B. Maszur, and K. Wingberg. The contributions are of exceptionally high quality, and this book will have permanent value. The volume will be of great interest to students and established workers in many areas of algebraic number theory and algebraic geometry
GrothendieckSerre correspondence by
A Grothendieck(
Book
)
25 editions published between 2001 and 2004 in 3 languages and held by 350 WorldCat member libraries worldwide
"The book is a bilingual (French and English) edition of the mathematical correspondence between A. Grothendieck and J.P. Serre. The original French text of 84 letters is supplemented here by the English translation, with French text printed on the lefthand pages and the corresponding English text printed on the righthand pages. The book also includes several facsimiles of original letters." "The letters presented in the book were mainly written between 1955 and 1965. During this period, algebraic geometry went through a remarkable transformation, and Grothendieck and Serre were among central figures in this process. The reader can follow the creation of some of the most important notions of modern mathematics, like sheaf cohomology, schernes, RiemannRoch type theorems, algebraic fundamental group, motives. The letters also reflect the mathematical and political atmosphere of this period (Bourbaki, Paris, Harvard, Princeton, war in Algeria, etc.) Also included are a few letters written between 1984 and 1987. The letters are supplemented by J.P. Serre's notes, which give explanations, corrections, and references further results." "The book should be useful to specialists in algebraic geometry, in history of mathematics, and to all mathematicians who want to understand how great mathematics is created."BOOK JACKET
25 editions published between 2001 and 2004 in 3 languages and held by 350 WorldCat member libraries worldwide
"The book is a bilingual (French and English) edition of the mathematical correspondence between A. Grothendieck and J.P. Serre. The original French text of 84 letters is supplemented here by the English translation, with French text printed on the lefthand pages and the corresponding English text printed on the righthand pages. The book also includes several facsimiles of original letters." "The letters presented in the book were mainly written between 1955 and 1965. During this period, algebraic geometry went through a remarkable transformation, and Grothendieck and Serre were among central figures in this process. The reader can follow the creation of some of the most important notions of modern mathematics, like sheaf cohomology, schernes, RiemannRoch type theorems, algebraic fundamental group, motives. The letters also reflect the mathematical and political atmosphere of this period (Bourbaki, Paris, Harvard, Princeton, war in Algeria, etc.) Also included are a few letters written between 1984 and 1987. The letters are supplemented by J.P. Serre's notes, which give explanations, corrections, and references further results." "The book should be useful to specialists in algebraic geometry, in history of mathematics, and to all mathematicians who want to understand how great mathematics is created."BOOK JACKET
Abelian l̳adic representations and elliptic curves; McGill University lecture notes by
JeanPierre Serre(
Book
)
7 editions published in 1968 in English and held by 335 WorldCat member libraries worldwide
7 editions published in 1968 in English and held by 335 WorldCat member libraries worldwide
Gesammelte Abhandlungen by
Ferdinand Georg Frobenius(
Book
)
18 editions published between 1968 and 2015 in 3 languages and held by 326 WorldCat member libraries worldwide
18 editions published between 1968 and 2015 in 3 languages and held by 326 WorldCat member libraries worldwide
Motives by Summer Research Conference on Motives(
Book
)
17 editions published between 1991 and 2012 in English and held by 325 WorldCat member libraries worldwide
17 editions published between 1991 and 2012 in English and held by 325 WorldCat member libraries worldwide
Abelian ladic representations and elliptic curves by
JeanPierre Serre(
Book
)
30 editions published between 1968 and 1998 in 3 languages and held by 301 WorldCat member libraries worldwide
This classic book contains an introduction to systems of ladic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent developments on the TaniyamaWeil conjecture and Fermat's Last Theorem. The initial chapters are devoted to the Abelian case (complex multiplication), where one finds a nice correspondence between the ladic representations and the linear representations of some algebraic groups (now called Taniyama groups) The last chapter handles the case of elliptic curves with no complex multiplication, the main result of which is that the image of the Galois group (in the corresponding ladic representation) is "large."
30 editions published between 1968 and 1998 in 3 languages and held by 301 WorldCat member libraries worldwide
This classic book contains an introduction to systems of ladic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent developments on the TaniyamaWeil conjecture and Fermat's Last Theorem. The initial chapters are devoted to the Abelian case (complex multiplication), where one finds a nice correspondence between the ladic representations and the linear representations of some algebraic groups (now called Taniyama groups) The last chapter handles the case of elliptic curves with no complex multiplication, the main result of which is that the image of the Galois group (in the corresponding ladic representation) is "large."
more
fewer
Audience Level
0 

1  
Kids  General  Special 
Related Identities
 Zagier, Don 1951 Other Editor
 Gabriel, Peter 1933 Other Author Redactor Editor Collector
 Colmez, Pierre Editor
 Kleiman, Steven L. Other Editor
 Jannsen, Uwe Other Author Editor
 Frobenius, Ferdinand Georg 18491917 Author
 Grothendieck, A. (Alexandre) Other Publishing director Author Editor
 Ihara, Y. (Yasutaka) 1938 Author Editor
 Ribet, Kenneth Other Editor
 Cartan, Henri 19042008 Publishing director Author
Useful Links
Associated Subjects
Abelian groups Abelian varieties Algebra Algebra, Homological Algebraic fields Algebraic number theory Algebraic varieties Analytic functions Brauer, Richard, Chow, WeiLiang, Class field theory Colmez, Pierre Curves, Algebraic Curves, Elliptic Dimension theory (Algebra) Diophantine analysis Finite groups Forms, Quadratic France Free groups Functions of complex variables Galois cohomology Galois theory Geometry, Algebraic Grothendieck, A.(Alexandre) Group theory Homology theory Lie algebras Lie groups Linear algebraic groups Local fields (Algebra) Local rings Mathematical analysis Mathematicians Mathematics Modular functions Modules (Algebra) Motives (Mathematics) Multiplicity (Mathematics) Number theory Representations of algebras Representations of groups Rings (Algebra) Serre, JeanPierre Serre, JeanPierre, Sheaf theory Tate, John Torrence, Topological groups Trees (Graph theory) Weil conjectures
Covers
Alternative Names
JeanPierre Serre Frans wiskundige
JeanPierre Serre fransk matematikar
JeanPierre Serre fransk matematiker
JeanPierre Serre französischer Mathematiker
JeanPierre Serre French mathematician
JeanPierre Serre matemàtic francès
JeanPierre Serre matematician francez
JeanPierre Serre matematico e accademico francese
JeanPierre Serre matemático francés
JeanPierre Serre matematik a topolog
JeanPierre Serre matematyk francuski
JeanPierre Serre mathématicien français
Serr, Ž.
Serr, Ž. 1926
Serr, Ž.P.
Serr, Z.P. 1926
Serr, Zh.P.
Serr, Zh.P. 1926
Serr, ZhanPʹer 1926
Serre, J.
Serre, J. 1926
Serre, J.P.
Serre, J.P. 1926
Serre, J. P. (Jean Pierre), 1926
Serre, Jean 1926
Serre, Jean P. 1926
Serre, JeanPierre
Serre, JeanPierre 1926
ЖанПьер Серр французский математик
ЖанП'єр Серр
Серр, Ж.П..
Серр, Ж.П 1926
ז'אןפייר סר
ז'אןפייר סר מתמטיקאי צרפתי
جانبيير سير
جانبيير سير رياضياتي فرنسي
جانپیری سیری
ژان پیر سر ریاضیدان فرانسوی
ژانپییر سر
ရောန်ဖြဲ ဆဲ
장피에르 세르
ジャン＝ピエール・セール
セール, J.P.
セール, ジャンーピエール
讓皮埃爾·塞爾
讓皮埃爾·塞爾 法國數學家
Languages