Neukirch, Jürgen 1937
Overview
Works:  23 works in 169 publications in 3 languages and 3,051 library holdings 

Genres:  History 
Roles:  Author, Editor, pre 
Classifications:  QA247, 512.7 
Publication Timeline
.
Most widely held works by
Jürgen Neukirch
Cohomology of number fields by
Jürgen Neukirch(
Book
)
30 editions published between 1999 and 2013 in English and Undetermined and held by 559 WorldCat member libraries worldwide
The second edition is a corrected and extended version of the first. It is a textbook for students, as well as a reference book for the working mathematician, on cohomological topics in number theory. The first part provides algebraic background: cohomology of profinite groups, duality groups, free products, and homotopy theory of modules, with new sections on spectral sequences and on Tate cohomology of profinite groups. The second part deals with Galois groups of local and global fields: Tate duality, structure of absolute Galois groups of local fields, extensions with restricted ramification, PoitouTate duality, Hasse principles, theorem of GrunwaldWang, Leopoldt's conjecture, Riemann's existence theorem, the theorems of Iwasawa and of Šafarevic on solvable groups as Galois groups, Iwasawa theory, and anabelian principles. New material is introduced here on duality theorems for unramified and tamely ramified extensions, a careful analysis of 2extensions of real number fields and a complete proof of Neukirch's theorem on solvable Galois groups with given local conditions. The present edition is a corrected printing of the 2008 edition
30 editions published between 1999 and 2013 in English and Undetermined and held by 559 WorldCat member libraries worldwide
The second edition is a corrected and extended version of the first. It is a textbook for students, as well as a reference book for the working mathematician, on cohomological topics in number theory. The first part provides algebraic background: cohomology of profinite groups, duality groups, free products, and homotopy theory of modules, with new sections on spectral sequences and on Tate cohomology of profinite groups. The second part deals with Galois groups of local and global fields: Tate duality, structure of absolute Galois groups of local fields, extensions with restricted ramification, PoitouTate duality, Hasse principles, theorem of GrunwaldWang, Leopoldt's conjecture, Riemann's existence theorem, the theorems of Iwasawa and of Šafarevic on solvable groups as Galois groups, Iwasawa theory, and anabelian principles. New material is introduced here on duality theorems for unramified and tamely ramified extensions, a careful analysis of 2extensions of real number fields and a complete proof of Neukirch's theorem on solvable Galois groups with given local conditions. The present edition is a corrected printing of the 2008 edition
Algebraic number theory by
Jürgen Neukirch(
Book
)
16 editions published between 1999 and 2010 in English and held by 510 WorldCat member libraries worldwide
"The present book has as its aim to resolve a discrepancy in the textbook literature and ... to provide a comprehensive introduction to algebraic number theory which is largely based on the modern, unifying conception of (onedimensional) arithmetic algebraic geometry. ... Despite this exacting program, the book remains an introduction to algebraic number theory for the beginner ... The author discusses the classical concepts from the viewpoint of Arakelov theory ... The treatment of class field theory is ... particularly rich in illustrating complements, hints for further study, and concrete examples ... The concluding chapter VII on zetafunctions and Lseries is another outstanding advantage of the present textbook ... The book is, without any doubt, the most uptodate, systematic, and theoretically comprehensive textbook on algebraic number field theory available." W. Kleinert in Z.blatt f. Math., 1992 "The author's enthusiasm for this topic is rarely as evident for the reader as in this book.  A good book, a beautiful book." F. Lorenz in Jber. DMV 1995 "The present work is written in a very careful and masterly fashion. It does not show the pains that it must have caused even an expert like Neukirch. It undoubtedly is liable to become a classic; the more so as recent developments have been taken into account which will not be outdated quickly. Not only must it be missing from the library of no number theorist, but it can simply be recommended to every mathematician who wants to get an idea of modern arithmetic." J. Schoissengeier in Montatshefte Mathematik 1994
16 editions published between 1999 and 2010 in English and held by 510 WorldCat member libraries worldwide
"The present book has as its aim to resolve a discrepancy in the textbook literature and ... to provide a comprehensive introduction to algebraic number theory which is largely based on the modern, unifying conception of (onedimensional) arithmetic algebraic geometry. ... Despite this exacting program, the book remains an introduction to algebraic number theory for the beginner ... The author discusses the classical concepts from the viewpoint of Arakelov theory ... The treatment of class field theory is ... particularly rich in illustrating complements, hints for further study, and concrete examples ... The concluding chapter VII on zetafunctions and Lseries is another outstanding advantage of the present textbook ... The book is, without any doubt, the most uptodate, systematic, and theoretically comprehensive textbook on algebraic number field theory available." W. Kleinert in Z.blatt f. Math., 1992 "The author's enthusiasm for this topic is rarely as evident for the reader as in this book.  A good book, a beautiful book." F. Lorenz in Jber. DMV 1995 "The present work is written in a very careful and masterly fashion. It does not show the pains that it must have caused even an expert like Neukirch. It undoubtedly is liable to become a classic; the more so as recent developments have been taken into account which will not be outdated quickly. Not only must it be missing from the library of no number theorist, but it can simply be recommended to every mathematician who wants to get an idea of modern arithmetic." J. Schoissengeier in Montatshefte Mathematik 1994
Class field theory by
Jürgen Neukirch(
Book
)
22 editions published between 1984 and 2012 in 3 languages and held by 493 WorldCat member libraries worldwide
Class field theory, which is so immediately compelling in its main assertions, has, ever since its invention, suffered from the fact that its proofs have required a complicated and, by comparison with the results, rather imper spicuous system of arguments which have tended to jump around all over the place. My earlier presentation of the theory [41] has strengthened me in the belief that a highly elaborate mechanism, such as, for example, cohomol ogy, might not be adequate for a numbertheoretical law admitting a very direct formulation, and that the truth of such a law must be susceptible to a far more immediate insight. I was determined to write the present, new account of class field theory by the discovery that, in fact, both the local and the global reciprocity laws may be subsumed under a purely group theoretical principle, admitting an entirely elementary description. This de scription makes possible a new foundation for the entire theory. The rapid advance to the main theorems of class field theory which results from this approach has made it possible to include in this volume the most important consequences and elaborations, and further related theories, with the excep tion of the cohomology version which I have this time excluded. This remains a significant variant, rich in application, but its principal results should be directly obtained from the material treated here
22 editions published between 1984 and 2012 in 3 languages and held by 493 WorldCat member libraries worldwide
Class field theory, which is so immediately compelling in its main assertions, has, ever since its invention, suffered from the fact that its proofs have required a complicated and, by comparison with the results, rather imper spicuous system of arguments which have tended to jump around all over the place. My earlier presentation of the theory [41] has strengthened me in the belief that a highly elaborate mechanism, such as, for example, cohomol ogy, might not be adequate for a numbertheoretical law admitting a very direct formulation, and that the truth of such a law must be susceptible to a far more immediate insight. I was determined to write the present, new account of class field theory by the discovery that, in fact, both the local and the global reciprocity laws may be subsumed under a purely group theoretical principle, admitting an entirely elementary description. This de scription makes possible a new foundation for the entire theory. The rapid advance to the main theorems of class field theory which results from this approach has made it possible to include in this volume the most important consequences and elaborations, and further related theories, with the excep tion of the cohomology version which I have this time excluded. This remains a significant variant, rich in application, but its principal results should be directly obtained from the material treated here
Algebraische Zahlentheorie by
Jürgen Neukirch(
Book
)
16 editions published between 1992 and 2012 in 3 languages and held by 233 WorldCat member libraries worldwide
Die algebraische Zahlentheorie ist eine der traditionsreichsten und gleichzeitig heute besonders aktuellen Grunddisziplinen der Mathematik. In dem vorliegenden Buch wird sie in einem ausführlichen und weitgefaßten Rahmen abgehandelt, der sowohl die Grundlagen als auch ihre Höhepunkte enthält. Die Darstellung führt den Leser in konkreter Weise in das Gebiet ein, läßt sich dabei von modernen Erkenntnissen übergeordneter Natur leiten und ist in vielen Teilen neu. Der grundlegende erste Teil ist mit einigen neuen Aspekten versehen, wie etwa einer ausführlichen Theorie der Ordnungen. Über die Grundlagen hinaus enthält das Buch eine geometrische Neubegründung der Theorie der algebraischen Zahlkörper durch die Entwicklung einer "RiemannRochTheorie" vom "Arakelovschen Standpunkt", die bis zu einem "GrothendieckRiemannRochTheorem" führt, ferner lokale und globale Klassenkörpertheorie und schließlich eine Darstellung der Theorie der Theta und LReihen, die die klassischen Arbeiten von Hecke in eine faßliche Form setzt. Das Buch wendet sich an Studenten nach dem Vordiplom bzw. Bachelor. Darüber hinaus ist es dem Forscher als weiterweisendes Handbuch unentbehrlich
16 editions published between 1992 and 2012 in 3 languages and held by 233 WorldCat member libraries worldwide
Die algebraische Zahlentheorie ist eine der traditionsreichsten und gleichzeitig heute besonders aktuellen Grunddisziplinen der Mathematik. In dem vorliegenden Buch wird sie in einem ausführlichen und weitgefaßten Rahmen abgehandelt, der sowohl die Grundlagen als auch ihre Höhepunkte enthält. Die Darstellung führt den Leser in konkreter Weise in das Gebiet ein, läßt sich dabei von modernen Erkenntnissen übergeordneter Natur leiten und ist in vielen Teilen neu. Der grundlegende erste Teil ist mit einigen neuen Aspekten versehen, wie etwa einer ausführlichen Theorie der Ordnungen. Über die Grundlagen hinaus enthält das Buch eine geometrische Neubegründung der Theorie der algebraischen Zahlkörper durch die Entwicklung einer "RiemannRochTheorie" vom "Arakelovschen Standpunkt", die bis zu einem "GrothendieckRiemannRochTheorem" führt, ferner lokale und globale Klassenkörpertheorie und schließlich eine Darstellung der Theorie der Theta und LReihen, die die klassischen Arbeiten von Hecke in eine faßliche Form setzt. Das Buch wendet sich an Studenten nach dem Vordiplom bzw. Bachelor. Darüber hinaus ist es dem Forscher als weiterweisendes Handbuch unentbehrlich
Klassenkörpertheorie by
Jürgen Neukirch(
Book
)
34 editions published between 1967 and 2011 in German and Undetermined and held by 197 WorldCat member libraries worldwide
34 editions published between 1967 and 2011 in German and Undetermined and held by 197 WorldCat member libraries worldwide
Class field theory : the Bonn Lectures by
Jürgen Neukirch(
Book
)
18 editions published between 1986 and 2013 in English and held by 73 WorldCat member libraries worldwide
The present manuscript is an improved edition of a text that first appeared under the same title in Bonner Mathematische Schriften, no.26, and originated from a series of lectures given by the author in 1965/66 in Wolfgang Krull's seminar in Bonn. Its main goal is to provide the reader, acquainted with the basics of algebraic number theory, a quick and immediate access to class field theory. This script consists of three parts, the first of which discusses the cohomology of finite groups. The second part discusses local class field theory, and the third part concerns the class field theory of finite algebraic number fields
18 editions published between 1986 and 2013 in English and held by 73 WorldCat member libraries worldwide
The present manuscript is an improved edition of a text that first appeared under the same title in Bonner Mathematische Schriften, no.26, and originated from a series of lectures given by the author in 1965/66 in Wolfgang Krull's seminar in Bonn. Its main goal is to provide the reader, acquainted with the basics of algebraic number theory, a quick and immediate access to class field theory. This script consists of three parts, the first of which discusses the cohomology of finite groups. The second part discusses local class field theory, and the third part concerns the class field theory of finite algebraic number fields
Über gewisse ausgezeichnete unendliche algebraische Zahlkörper by
Jürgen Neukirch(
Book
)
11 editions published in 1965 in German and Undetermined and held by 67 WorldCat member libraries worldwide
11 editions published in 1965 in German and Undetermined and held by 67 WorldCat member libraries worldwide
Ansichten über die LanglandsVermutung by
Jürgen Neukirch(
Book
)
4 editions published between 1982 and 1983 in German and held by 14 WorldCat member libraries worldwide
4 editions published between 1982 and 1983 in German and held by 14 WorldCat member libraries worldwide
Numbers by
HeinzDieter Ebbinghaus(
)
1 edition published in 1991 in English and held by 6 WorldCat member libraries worldwide
1 edition published in 1991 in English and held by 6 WorldCat member libraries worldwide
Lokale Klassenkörpertheorie, cohomologisch behandelt by
KarlOtto Stöhr(
Book
)
1 edition published in 1966 in German and held by 4 WorldCat member libraries worldwide
1 edition published in 1966 in German and held by 4 WorldCat member libraries worldwide
IwasawaTheorie : 14.10. bis 20.10.1979(
Book
)
2 editions published in 1979 in German and held by 3 WorldCat member libraries worldwide
2 editions published in 1979 in German and held by 3 WorldCat member libraries worldwide
Algebraische Zahlentheorie by
Jürgen Neukirch(
)
1 edition published in 2006 in German and held by 2 WorldCat member libraries worldwide
1 edition published in 2006 in German and held by 2 WorldCat member libraries worldwide
Klassenkoerpertheorie by
Jürgen Neukirch(
Book
)
1 edition published in 1967 in German and held by 1 WorldCat member library worldwide
1 edition published in 1967 in German and held by 1 WorldCat member library worldwide
Klassenkörpertheorie by
Jürgen Neukirch(
Book
)
1 edition published in 1967 in German and held by 1 WorldCat member library worldwide
1 edition published in 1967 in German and held by 1 WorldCat member library worldwide
On values of zeta functions and ladic Euler characteristics by
Pilar Bayer i Isant(
Book
)
1 edition published in 1979 in German and held by 1 WorldCat member library worldwide
1 edition published in 1979 in German and held by 1 WorldCat member library worldwide
Klassenkörpertheorie : Vol.:1: Cohomologie der endlichen Gruppen : Vol.: 2: Lokale Klassenkörpertheorie : Vol.: 3: Globale
Klassenkörpertheorie(
Book
)
1 edition published in 1967 in Undetermined and held by 1 WorldCat member library worldwide
1 edition published in 1967 in Undetermined and held by 1 WorldCat member library worldwide
Numbers by
HeinzDieter Ebbinghaus(
Book
)
2 editions published between 1990 and 1991 in English and held by 1 WorldCat member library worldwide
This is a book about numbers  all kinds of numbers, from integers to padics, from rationals to octonions, from reals to infinitesimals. Who first used the standard notation for Â? Why was Hamilton obsessed with quaternions? What was the prospect for "quaternionic analysis" in the 19th century? This is the story about one of the major threads of mathematics over thousands of years. It is a story that will give the reader both a glimpse of the mystery surrounding imaginary numbers in the 17th century and also a view of some major developments in the 20th
2 editions published between 1990 and 1991 in English and held by 1 WorldCat member library worldwide
This is a book about numbers  all kinds of numbers, from integers to padics, from rationals to octonions, from reals to infinitesimals. Who first used the standard notation for Â? Why was Hamilton obsessed with quaternions? What was the prospect for "quaternionic analysis" in the 19th century? This is the story about one of the major threads of mathematics over thousands of years. It is a story that will give the reader both a glimpse of the mystery surrounding imaginary numbers in the 17th century and also a view of some major developments in the 20th
Über eine Charakterisierung des Körpers aller algebraischen padischen Zahlen by
Jürgen Neukirch(
Book
)
1 edition published in 1968 in German and held by 1 WorldCat member library worldwide
1 edition published in 1968 in German and held by 1 WorldCat member library worldwide
Arithmetik der Abelschen Zahlkörper und Klassenkörper der komplexen Multiplikation 25.3 bis 31.3.1979(
Book
)
1 edition published in 1979 in German and held by 1 WorldCat member library worldwide
1 edition published in 1979 in German and held by 1 WorldCat member library worldwide
Zahlen by
HeinzDieter Ebbinghaus(
)
2 editions published between 1988 and 1992 in German and held by 0 WorldCat member libraries worldwide
Die Schwierigkeit Mathematik zu lernen und zu lehren ist jedem bekannt, der einmal mit diesem Fach in Berührung gekommen ist. Begriffe wie "reelle oder komplexe Zahlen, Pi" sind zwar jedem geläufig, aber nur wenige wissen, was sich wirklich dahinter verbirgt. Die Autoren dieses Bandes geben jedem, der mehr wissen will als nur die Hülle der Begriffe, eine meisterhafte Einführung in die Magie der Mathematik und schlagen einzigartige Brücken für Studenten. Die Rezensenten der ersten beiden Auflagen überschlugen sich
2 editions published between 1988 and 1992 in German and held by 0 WorldCat member libraries worldwide
Die Schwierigkeit Mathematik zu lernen und zu lehren ist jedem bekannt, der einmal mit diesem Fach in Berührung gekommen ist. Begriffe wie "reelle oder komplexe Zahlen, Pi" sind zwar jedem geläufig, aber nur wenige wissen, was sich wirklich dahinter verbirgt. Die Autoren dieses Bandes geben jedem, der mehr wissen will als nur die Hülle der Begriffe, eine meisterhafte Einführung in die Magie der Mathematik und schlagen einzigartige Brücken für Studenten. Die Rezensenten der ersten beiden Auflagen überschlugen sich
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Jürgen Neukirch Duits wiskundige
Jürgen Neukirch German mathematician
Jürgen Neukirch mathématicien allemand
Jürgen Neukirch tysk matematikar
Jürgen Neukirch tysk matematiker
Neukirch, J.
Neukirch, Jurgen 19371997
Noikiruhi, J. 19371997
위르겐 노이키르히
ノイキルヒ, J.
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