Neukirch, Jürgen 1937
Overview
Works:  25 works in 151 publications in 3 languages and 2,660 library holdings 

Genres:  History 
Roles:  Author, Editor 
Classifications:  QA247, 512.7 
Publication Timeline
.
Most widely held works by
Jürgen Neukirch
Class field theory
by
Jürgen Neukirch(
Book
)
60 editions published between 1967 and 2013 in 3 languages and held by 1,046 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
60 editions published between 1967 and 2013 in 3 languages and held by 1,046 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
Cohomology of number fields
by
Jürgen Neukirch(
Book
)
25 editions published between 1999 and 2013 in English and held by 761 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, Leopoldts conjecture, Riemanns existence theorem, the theorems of Iwasawa and of afarevic 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 Neukirchs theorem on solvable Galois groups with given local conditions. The present edition is a corrected printing of the 2008 edition
25 editions published between 1999 and 2013 in English and held by 761 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, Leopoldts conjecture, Riemanns existence theorem, the theorems of Iwasawa and of afarevic 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 Neukirchs 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
)
14 editions published between 1999 and 2011 in English and held by 502 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
14 editions published between 1999 and 2011 in English and held by 502 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
Algebraische Zahlentheorie
by
Jürgen Neukirch(
)
15 editions published between 1992 and 2007 in German and Undetermined and held by 227 WorldCat member libraries worldwide
15 editions published between 1992 and 2007 in German and Undetermined and held by 227 WorldCat member libraries worldwide
Über gewisse ausgezeichnete unendliche algebraische Zahlkörper
by
Jürgen Neukirch(
Book
)
9 editions published in 1965 in German and Undetermined and held by 61 WorldCat member libraries worldwide
9 editions published in 1965 in German and Undetermined and held by 61 WorldCat member libraries worldwide
Numbers
by
HeinzDieter Ebbinghaus(
)
3 editions published between 1990 and 1992 in English and German and held by 19 WorldCat member libraries 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
3 editions published between 1990 and 1992 in English and German and held by 19 WorldCat member libraries 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
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
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
Klassenkörpertheorie : Teil 1: Cohomologie der endlichen Gruppen, Teil 2: Lokale Klassenkörpertheorie, Teil 3: Globale Klassenkörpertheorie
by
Jürgen Neukirch(
Book
)
1 edition published in 1967 in German and held by 3 WorldCat member libraries worldwide
1 edition published in 1967 in German and held by 3 WorldCat member libraries worldwide
Daisūteki seisūron
(
Book
)
2 editions published between 2003 and 2012 in Japanese and held by 3 WorldCat member libraries worldwide
2 editions published between 2003 and 2012 in Japanese and held by 3 WorldCat member libraries worldwide
Klassenkoerpertheorie
by
Jürgen Neukirch(
Book
)
2 editions published between 1967 and 1969 in German and held by 2 WorldCat member libraries worldwide
2 editions published between 1967 and 1969 in German and held by 2 WorldCat member libraries worldwide
Der Villinger Stadtwald
by
Jürgen Neukirch(
Book
)
1 edition published in 1908 in German and held by 2 WorldCat member libraries worldwide
1 edition published in 1908 in German and held by 2 WorldCat member libraries worldwide
Class Field Theory The Bonn Lectures Edited by Alexander Schmidt
by
Jürgen Neukirch(
)
1 edition published in 2013 in English and held by 2 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
1 edition published in 2013 in English and held by 2 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
Gedächnißrede für das hochsel. Königs Friedrich Wilhelm III. Maj. [um 19. Jul. umgefalten in der _ Stadt_Kirche]
by
Jürgen Neukirch(
Book
)
1 edition published in 1840 in German and held by 1 WorldCat member library worldwide
1 edition published in 1840 in German and held by 1 WorldCat member library worldwide
Ueber gewisse ausgezeignete unendliche algebraische zahlkoerper
by
Jürgen Neukirch(
Book
)
1 edition published in 1965 in German and held by 1 WorldCat member library worldwide
1 edition published in 1965 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
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
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
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
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