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Titlebook: Galois Theory of p-Extensions; Helmut Koch Book 2002 Springer-Verlag Berlin Heidelberg 2002 Cohomology.Prime.algebra.chomology of groups.c

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發(fā)表于 2025-3-21 18:06:22 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Galois Theory of p-Extensions
編輯Helmut Koch
視頻videohttp://file.papertrans.cn/381/380429/380429.mp4
概述Helmut Koch‘s classic now becomes available in English.Competently translated by Franz Lemmermeyer.Introduces the theory of pro-p groups and their cohomology.Contains a postscript on the recent develo
叢書名稱Springer Monographs in Mathematics
圖書封面Titlebook: Galois Theory of p-Extensions;  Helmut Koch Book 2002 Springer-Verlag Berlin Heidelberg 2002 Cohomology.Prime.algebra.chomology of groups.c
描述First published in German in 1970 and translated into Russian in 1973, this classic now becomes available in English. After introducing the theory of pro-p groups and their cohomology, it discusses presentations of the Galois groups G S of maximal .p.-extensions of number fields that are unramified outside a given set S of primes. It computes generators and relations as well as the cohomological dimension of some G S, and gives applications to infinite class field towers.The book demonstrates that the cohomology of groups is very useful for studying Galois theory of number fields; at the same time, it offers a down to earth introduction to the cohomological method. In a "Postscript" Helmut Koch and Franz Lemmermeyer give a survey on the development of the field in the last 30 years. Also, a list of additional, recent references has been included.
出版日期Book 2002
關(guān)鍵詞Cohomology; Prime; algebra; chomology of groups; class field towers; number theory; pro-p groups
版次1
doihttps://doi.org/10.1007/978-3-662-04967-9
isbn_softcover978-3-642-07817-0
isbn_ebook978-3-662-04967-9Series ISSN 1439-7382 Series E-ISSN 2196-9922
issn_series 1439-7382
copyrightSpringer-Verlag Berlin Heidelberg 2002
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沙發(fā)
發(fā)表于 2025-3-21 23:04:25 | 只看該作者
Group Algebras of pro-, Groups,the complete group algebra of a pro-. group. In this chapter, . will always denote a compact commutative ring with identity. For finite groups ., the additive group of the group ring .[.] is isomorphic to the direct sum of #. copies of ., and thus inherits a topology that makes .[.] into a compact g
板凳
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地板
發(fā)表于 2025-3-22 05:38:17 | 只看該作者
Cohomology of Profinite Groups,rements for Galois cohomology into consideration, whereas the cohomology of finite groups that is needed for class field theory is only developed as far as is necessary for the formulation of the theorems that will be important for us. See also J.P. Serre [51, Chap. VI–XI].
5#
發(fā)表于 2025-3-22 11:28:18 | 只看該作者
1439-7382 their cohomology.Contains a postscript on the recent develoFirst published in German in 1970 and translated into Russian in 1973, this classic now becomes available in English. After introducing the theory of pro-p groups and their cohomology, it discusses presentations of the Galois groups G S of
6#
發(fā)表于 2025-3-22 16:15:34 | 只看該作者
https://doi.org/10.1007/978-3-663-14669-8rements for Galois cohomology into consideration, whereas the cohomology of finite groups that is needed for class field theory is only developed as far as is necessary for the formulation of the theorems that will be important for us. See also J.P. Serre [51, Chap. VI–XI].
7#
發(fā)表于 2025-3-22 21:07:07 | 只看該作者
Book 2002pro-p groups and their cohomology, it discusses presentations of the Galois groups G S of maximal .p.-extensions of number fields that are unramified outside a given set S of primes. It computes generators and relations as well as the cohomological dimension of some G S, and gives applications to in
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10#
發(fā)表于 2025-3-23 08:26:03 | 只看該作者
Helmut KochHelmut Koch‘s classic now becomes available in English.Competently translated by Franz Lemmermeyer.Introduces the theory of pro-p groups and their cohomology.Contains a postscript on the recent develo
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