Parshin, A. N.
Overview
Works:  65 works in 298 publications in 4 languages and 3,200 library holdings 

Genres:  Conference papers and proceedings Textbooks Sources History Records and correspondence 
Roles:  Editor, Author, Interviewee, Redactor, Translator 
Classifications:  QA564, 512 
Publication Timeline
.
Most widely held works by
A. N Parshin
Basic algebraic geometry by
I. R Shafarevich(
Book
)
46 editions published between 1994 and 2010 in English and German and held by 610 WorldCat member libraries worldwide
This volume of the Encyclopaedia contains two contributions on closely related subjects: the theory of linear algebraic groups and invariant theory. The first part is written by T.A. Springer, a wellknown expert in the first mentioned field. He presents a comprehensive survey, which contains numerous sketched proofs and he discusses the particular features of algebraic groups over special fields (finite, local, and global). The authors of part two, E.B. Vinberg and V.L. Popov, are among the most active researchers in invariant theory. The last 20 years have been a period of vigorous development in this field due to the influence of modern methods from algebraic geometry. The book will be very useful as a reference and research guide to graduate students and researchers in mathematics and theoretical physics
46 editions published between 1994 and 2010 in English and German and held by 610 WorldCat member libraries worldwide
This volume of the Encyclopaedia contains two contributions on closely related subjects: the theory of linear algebraic groups and invariant theory. The first part is written by T.A. Springer, a wellknown expert in the first mentioned field. He presents a comprehensive survey, which contains numerous sketched proofs and he discusses the particular features of algebraic groups over special fields (finite, local, and global). The authors of part two, E.B. Vinberg and V.L. Popov, are among the most active researchers in invariant theory. The last 20 years have been a period of vigorous development in this field due to the influence of modern methods from algebraic geometry. The book will be very useful as a reference and research guide to graduate students and researchers in mathematics and theoretical physics
Number theory II : algebraic number theory by
Helmut Koch(
Book
)
26 editions published between 1991 and 1992 in 3 languages and held by 359 WorldCat member libraries worldwide
From the reviews of the first printing, published as Volume 62 of the Encyclopaedia of Mathematical Sciences: " ... The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes." Monatshefte fuer Mathematik, 1994 " ... Koch's book is written mostly for nonspecialists. It is an uptodate account of the subject dealing with mostly general questions. Special results appear only as illustrating examples for the general features of the theory. It is supposed that the reader has good general background in the fields of modern (abstract) algebra and elementary number theory. We recommend this volume mainly to graduate studens and research mathematicians." Acta Scientiarum Mathematicarum, 1993
26 editions published between 1991 and 1992 in 3 languages and held by 359 WorldCat member libraries worldwide
From the reviews of the first printing, published as Volume 62 of the Encyclopaedia of Mathematical Sciences: " ... The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes." Monatshefte fuer Mathematik, 1994 " ... Koch's book is written mostly for nonspecialists. It is an uptodate account of the subject dealing with mostly general questions. Special results appear only as illustrating examples for the general features of the theory. It is supposed that the reader has good general background in the fields of modern (abstract) algebra and elementary number theory. We recommend this volume mainly to graduate studens and research mathematicians." Acta Scientiarum Mathematicarum, 1993
Number theory I : fundamental problems, ideas and theories by
I︠U︡. I Manin(
Book
)
33 editions published between 1992 and 1995 in English and Undetermined and held by 325 WorldCat member libraries worldwide
This book surveys from a unified point of view both the modern state and the trends of continuing development of various branches of number theory. Motivated by elementary problems (including some modern areas such as cryptography, factorization and primality testing), the central ideas of modern theories are exposed: algebraic number theory, calculations and properties of Galois groups, nonAbelian generalizations of class field theory, recursive computability and links with Diophantine equations, the arithmetic of algebraic varieties, connections with modular forms, zeta and Lfunctions. The authors have tried to present the most significant results and methods of modern time. An overview of the major conjectures is also given in order to illustrate current thinking in number theory. Most of these conjectures are based on analogies between functions and numbers, and on connections with other branches of mathematics such as algebraic topology, analysis, representation theory and geometry
33 editions published between 1992 and 1995 in English and Undetermined and held by 325 WorldCat member libraries worldwide
This book surveys from a unified point of view both the modern state and the trends of continuing development of various branches of number theory. Motivated by elementary problems (including some modern areas such as cryptography, factorization and primality testing), the central ideas of modern theories are exposed: algebraic number theory, calculations and properties of Galois groups, nonAbelian generalizations of class field theory, recursive computability and links with Diophantine equations, the arithmetic of algebraic varieties, connections with modular forms, zeta and Lfunctions. The authors have tried to present the most significant results and methods of modern time. An overview of the major conjectures is also given in order to illustrate current thinking in number theory. Most of these conjectures are based on analogies between functions and numbers, and on connections with other branches of mathematics such as algebraic topology, analysis, representation theory and geometry
Algebraic geometry V : fano varieties by
V. A Iskovskikh(
Book
)
15 editions published between 1994 and 2010 in English and held by 259 WorldCat member libraries worldwide
15 editions published between 1994 and 2010 in English and held by 259 WorldCat member libraries worldwide
Algebraic number theory and algebraic geometry : papers dedicated to A.N. Parshin on the occasion of his sixtieth birthday(
Book
)
6 editions published in 2002 in English and held by 204 WorldCat member libraries worldwide
6 editions published in 2002 in English and held by 204 WorldCat member libraries worldwide
Algebra by
B. L. van der Waerden(
Book
)
8 editions published in 1990 in English and Undetermined and held by 119 WorldCat member libraries worldwide
Contains a tutorial to help master the fundamental concepts of Algebra from monomials, inequalities, and coordinate geometry to functions and variations and word problems
8 editions published in 1990 in English and Undetermined and held by 119 WorldCat member libraries worldwide
Contains a tutorial to help master the fundamental concepts of Algebra from monomials, inequalities, and coordinate geometry to functions and variations and word problems
Algebra and analysis : proceedings of the International Centennial Chebotarev Conference held in Kazan, Russia, June 511,
1994 by International Centennial Chebotarev Conference(
Book
)
6 editions published in 1996 in English and held by 72 WorldCat member libraries worldwide
6 editions published in 1996 in English and held by 72 WorldCat member libraries worldwide
Algebra VI : combinatorial and asymptotic methods of algebra : nonassociative structures by
A. I Kostrikin(
Book
)
3 editions published between 1990 and 1995 in English and held by 60 WorldCat member libraries worldwide
3 editions published between 1990 and 1995 in English and held by 60 WorldCat member libraries worldwide
Number theory(
Book
)
7 editions published between 1992 and 1995 in English and Russian and held by 23 WorldCat member libraries worldwide
7 editions published between 1992 and 1995 in English and Russian and held by 23 WorldCat member libraries worldwide
Seminar Russkai︠a︡ filosofii︠a︡: tradit︠s︡ii︠a︡ i sovremennostʹ : 20042009 by
A. N Parshin(
Book
)
3 editions published between 2011 and 2012 in Russian and held by 21 WorldCat member libraries worldwide
3 editions published between 2011 and 2012 in Russian and held by 21 WorldCat member libraries worldwide
Algebraic geometry II : cohomology of algebraic varieties, algebraic surfaces(
Book
)
5 editions published between 1994 and 1996 in English and held by 16 WorldCat member libraries worldwide
This EMS volume consists of two parts. The first part is devoted to the exposition of the cohomology theory of algebraic varieties. The second part deals with algebraic surfaces. The authors, who are wellknown experts in the field, have taken pains to present the material rigorously and coherently. The book contains numerous examples and insights on various topics. This book will be immensely useful to mathematicians and graduate students working in algebraic geometry, arithmetic algebraic geometry, complex analysis and related fields
5 editions published between 1994 and 1996 in English and held by 16 WorldCat member libraries worldwide
This EMS volume consists of two parts. The first part is devoted to the exposition of the cohomology theory of algebraic varieties. The second part deals with algebraic surfaces. The authors, who are wellknown experts in the field, have taken pains to present the material rigorously and coherently. The book contains numerous examples and insights on various topics. This book will be immensely useful to mathematicians and graduate students working in algebraic geometry, arithmetic algebraic geometry, complex analysis and related fields
Rossiĭskai︠a︡ akademii︠a︡ nauk : Khronika protesta : Ii︠u︡nʹii︠u︡lʹ 2013 g. : Moskva, SanktPeterburg, Novosibirsk, Ekaterinburg,
Vladivostok, Kazanʹ, RostovnaDonu, Pushchino, Troit︠s︡k, Irkutsk, Nizhniĭ Novgorod, Tomsk, Apatity, Ufa, Chernogolovka,
Obninsk, Fri︠a︡zino, Borok, Syktyvkar, Tolʹi︠a︡tti, Saratov, Vologda, Chita, Makhachkala, Vladikavkaz, Nalʹchik(
Book
)
6 editions published in 2013 in Russian and held by 15 WorldCat member libraries worldwide
6 editions published in 2013 in Russian and held by 15 WorldCat member libraries worldwide
Transcendental numbers(
Book
)
3 editions published between 1997 and 1998 in English and held by 13 WorldCat member libraries worldwide
3 editions published between 1997 and 1998 in English and held by 13 WorldCat member libraries worldwide
Linear algebraic groups, invariant theory(
Book
)
3 editions published in 1994 in English and German and held by 11 WorldCat member libraries worldwide
3 editions published in 1994 in English and German and held by 11 WorldCat member libraries worldwide
Number theory III : diophantine geometry by
Serge Lang(
Book
)
7 editions published between 1991 and 1992 in English and Undetermined and held by 11 WorldCat member libraries worldwide
From the reviews of the first printing of this book, published as Volume 60 of the Encyclopaedia of Mathematical Sciences: "Between number theory and geometry there have been several stimulating influences, and this book records of these enterprises. This author, who has been at the centre of such research for many years, is one of the best guides a reader can hope for. The book is full of beautiful results, open questions, stimulating conjectures and suggestions where to look for future developments. This volume bears witness of the broad scope of knowledge of the author, and the influence of several people who have commented on the manuscript before publication ... Although in the series of number theory, this volume is on diophantine geometry, and the reader will notice that algebraic geometry is present in every chapter. ... The style of the book is clear. Ideas are well explained, and the author helps the reader to pass by several technicalities. Reading and rereading this book I noticed that the topics are treated in a nice, coherent way, however not in a historically logical order. ... The author writes "At the moment of writing, the situation is in flux ... ". That is clear from the scope of this book. In the area described many conjectures, important results, new developments took place in the last 30 years. And still new results come at a breathtaking speed in this rich field. In the introduction the author notices: "I have included several connections of diophantine geometry with other parts of mathematics, such as PDE and Laplacians, complex analysis, and differential geometry. A grand unification is going on, with multiple connections between these fields." Such a unification becomes clear in this beautiful book, which we recommend for mathematicians of all disciplines." Medelingen van het wiskundig genootschap, 1994 " ... It is fascinating to see how geometry, arithmetic and complex analysis grow together! ..." Monatshefte fr Mathematik, 1993
7 editions published between 1991 and 1992 in English and Undetermined and held by 11 WorldCat member libraries worldwide
From the reviews of the first printing of this book, published as Volume 60 of the Encyclopaedia of Mathematical Sciences: "Between number theory and geometry there have been several stimulating influences, and this book records of these enterprises. This author, who has been at the centre of such research for many years, is one of the best guides a reader can hope for. The book is full of beautiful results, open questions, stimulating conjectures and suggestions where to look for future developments. This volume bears witness of the broad scope of knowledge of the author, and the influence of several people who have commented on the manuscript before publication ... Although in the series of number theory, this volume is on diophantine geometry, and the reader will notice that algebraic geometry is present in every chapter. ... The style of the book is clear. Ideas are well explained, and the author helps the reader to pass by several technicalities. Reading and rereading this book I noticed that the topics are treated in a nice, coherent way, however not in a historically logical order. ... The author writes "At the moment of writing, the situation is in flux ... ". That is clear from the scope of this book. In the area described many conjectures, important results, new developments took place in the last 30 years. And still new results come at a breathtaking speed in this rich field. In the introduction the author notices: "I have included several connections of diophantine geometry with other parts of mathematics, such as PDE and Laplacians, complex analysis, and differential geometry. A grand unification is going on, with multiple connections between these fields." Such a unification becomes clear in this beautiful book, which we recommend for mathematicians of all disciplines." Medelingen van het wiskundig genootschap, 1994 " ... It is fascinating to see how geometry, arithmetic and complex analysis grow together! ..." Monatshefte fr Mathematik, 1993
Algebraic geometry I : complex projective varieties by
David Mumford(
Book
)
4 editions published between 1994 and 2007 in English and held by 6 WorldCat member libraries worldwide
Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevichs book is a must.'' The third edition, in addition to some minor corrections, now offers a new treatment of the RiemannRoch theorem for curves, including a proof from first principles. Shafarevich's book is an attractive and accessible introduction to algebraic geometry, suitable for beginning students and nonspecialists, and the new edition is set to remain a popular introduction to the field
4 editions published between 1994 and 2007 in English and held by 6 WorldCat member libraries worldwide
Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevichs book is a must.'' The third edition, in addition to some minor corrections, now offers a new treatment of the RiemannRoch theorem for curves, including a proof from first principles. Shafarevich's book is an attractive and accessible introduction to algebraic geometry, suitable for beginning students and nonspecialists, and the new edition is set to remain a popular introduction to the field
Algebra II : noncommutative rings, identities by
A. I Kostrikin(
Book
)
in English and held by 1 WorldCat member library worldwide
The algebra of square matrices of size n ~ 2 over the field of complex numbers is, evidently, the bestknown example of a noncommutative alge 1 bra  Subalgebras and subrings of this algebra (for example, the ring of n x n matrices with integral entries) arise naturally in many areas of mathemat ics. Historically however, the study of matrix algebras was preceded by the discovery of quatemions which, introduced in 1843 by Hamilton, found ap plications in the classical mechanics of the past century. Later it turned out that quaternion analysis had important applications in field theory. The al gebra of quaternions has become one of the classical mathematical objects; it is used, for instance, in algebra, geometry and topology. We will briefly focus on other examples of noncommutative rings and algebras which arise naturally in mathematics and in mathematical physics. The exterior algebra (or Grassmann algebra) is widely used in differential geometry  for example, in geometric theory of integration. Clifford algebras, which include exterior algebras as a special case, have applications in rep resentation theory and in algebraic topology. The Weyl algebra (Le. algebra of differential operators with· polynomial coefficients) often appears in the representation theory of Lie algebras. In recent years modules over the Weyl algebra and sheaves of such modules became the foundation of the socalled microlocal analysis. The theory of operator algebras (Le
in English and held by 1 WorldCat member library worldwide
The algebra of square matrices of size n ~ 2 over the field of complex numbers is, evidently, the bestknown example of a noncommutative alge 1 bra  Subalgebras and subrings of this algebra (for example, the ring of n x n matrices with integral entries) arise naturally in many areas of mathemat ics. Historically however, the study of matrix algebras was preceded by the discovery of quatemions which, introduced in 1843 by Hamilton, found ap plications in the classical mechanics of the past century. Later it turned out that quaternion analysis had important applications in field theory. The al gebra of quaternions has become one of the classical mathematical objects; it is used, for instance, in algebra, geometry and topology. We will briefly focus on other examples of noncommutative rings and algebras which arise naturally in mathematics and in mathematical physics. The exterior algebra (or Grassmann algebra) is widely used in differential geometry  for example, in geometric theory of integration. Clifford algebras, which include exterior algebras as a special case, have applications in rep resentation theory and in algebraic topology. The Weyl algebra (Le. algebra of differential operators with· polynomial coefficients) often appears in the representation theory of Lie algebras. In recent years modules over the Weyl algebra and sheaves of such modules became the foundation of the socalled microlocal analysis. The theory of operator algebras (Le
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Algebra Algebra, Abstract Algebra, Homological Algebraic number theory Algebraic varieties Algorithms Combinatorial analysis Computer scienceMathematics Curves, Algebraic Data encryption (Computer science) Determinants Diophantine analysis Diophantine equations Field theory (Physics) Geometry, Algebraic Group theory Hodge theory Homology theory Invariants Jacobians Ktheory Linear algebraic groups Logic, Symbolic and mathematical Manifolds (Mathematics) Mathematical analysis Mathematical physics Mathematics Modules (Algebra) Monoids Nonassociative algebras Noncommutative rings Number theory Philosophy Philosophy, Russian Physics Polynomials Protest movements Public opinion Research Rings (Algebra) Rossiĭskai︠a︡ akademii︠a︡ nauk Russia Russia (Federation) Schemes (Algebraic geometry) Scientists Shmidt, Otto I︠U︡lʹevich, Surfaces, Algebraic Topological groups Transcendental numbers Vector spaces
Alternative Names
Aleksej Nikolaevič Paršin
Alexei Nikolaevich Parshin Russian mathematician
Alexei Nikolajewitsch Parschin mathématicien russe
Alexei Nikolajewitsch Parschin Russisch wiskundige
Alexei Nikolajewitsch Parschin russischer Mathematiker
Parschin, Alexei Nikolajewitsch 1942
Parshin, A. N.
Parshin, A.N. 1942
Parshin, Alekseĭ Nikolaevich
Parshin, Aleksey Nikolaevich
Parshin, Aleksey Nikolaevich 1942
Parshin, Alexei N.
Parshin, Alexei Nikolaevich
Paršin, A. N.
Paršin, A. N. 1942
Paršin, Aleksej N. 1942
Pars̆in, Alexej Nikolaevic̆
Паршин, Алексей Николаевич 1942...
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