東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Galois cohomology and class field theory

Harari, David.

FindBook

Google Book

Amazon

博客來

Galois cohomology and class field theory

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Galois cohomology and class field theory/ by David Harari.
作者:	Harari, David.
出版者:	Cham :Springer International Publishing : : 2020.,
面頁冊數:	xiv, 338 p. :ill., digital ;24 cm.
內容註:	Preface -- Part I Group cohomology and Galois cohomology: generalities -- 1 Cohomology of finite groups -- 2 Cohomology of cyclic groups -- 3 p-groups, the Tate-Nakayama theorem -- 4 Cohomology of profinite groups -- 5 Cohomological dimension -- 6 First notions of Galois cohomology -- Part II Local fields -- 7 Basic facts about local fields -- 8 Brauer group of a local field -- 9 Local class field theory: the reciprocity law -- 10 The Tate local duality theorem -- 11 Local class field theory: Lubin-Tate theory -- Part III Global fields -- 12 Basic facts about global fields -- 13 Cohomology of the ideles -- 14 Reciprocity law -- 15 The abelianized absolute Galois group of a global field -- Part IV Duality theorems -- 16 Class formations -- 17 Poitou-Tate duality -- 18 Some applications -- Appendix -- A Some results from homological algebra -- B A survey of analytic methods -- References -- Index.
Contained By:	Springer eBooks
標題:	Galois cohomology. -
電子資源:	https://doi.org/10.1007/978-3-030-43901-9
ISBN:	9783030439019

Galois cohomology and class field theory
Harari, David.

Galois cohomology and class field theory[electronic resource] /by David Harari. - Cham :Springer International Publishing :2020. - xiv, 338 p. :ill., digital ;24 cm. - Universitext,0172-5939. - Universitext..

Preface -- Part I Group cohomology and Galois cohomology: generalities -- 1 Cohomology of finite groups -- 2 Cohomology of cyclic groups -- 3 p-groups, the Tate-Nakayama theorem -- 4 Cohomology of profinite groups -- 5 Cohomological dimension -- 6 First notions of Galois cohomology -- Part II Local fields -- 7 Basic facts about local fields -- 8 Brauer group of a local field -- 9 Local class field theory: the reciprocity law -- 10 The Tate local duality theorem -- 11 Local class field theory: Lubin-Tate theory -- Part III Global fields -- 12 Basic facts about global fields -- 13 Cohomology of the ideles -- 14 Reciprocity law -- 15 The abelianized absolute Galois group of a global field -- Part IV Duality theorems -- 16 Class formations -- 17 Poitou-Tate duality -- 18 Some applications -- Appendix -- A Some results from homological algebra -- B A survey of analytic methods -- References -- Index.

This graduate textbook offers an introduction to modern methods in number theory. It gives a complete account of the main results of class field theory as well as the Poitou-Tate duality theorems, considered crowning achievements of modern number theory. Assuming a first graduate course in algebra and number theory, the book begins with an introduction to group and Galois cohomology. Local fields and local class field theory, including Lubin-Tate formal group laws, are covered next, followed by global class field theory and the description of abelian extensions of global fields. The final part of the book gives an accessible yet complete exposition of the Poitou-Tate duality theorems. Two appendices cover the necessary background in homological algebra and the analytic theory of Dirichlet L-series, including the Cebotarev density theorem. Based on several advanced courses given by the author, this textbook has been written for graduate students. Including complete proofs and numerous exercises, the book will also appeal to more experienced mathematicians, either as a text to learn the subject or as a reference.

ISBN: 9783030439019

Standard No.: 10.1007/978-3-030-43901-9doiSubjects--Topical Terms:

888612
Galois cohomology.

LC Class. No.: QA612.3 / .H373 2020

Dewey Class. No.: 514.23

Galois cohomology and class field theory
LDR:03120nmm a2200349 a 4500 001 2221269
003 DE-He213
005 20201030091927.0
006 m d
007 cr nn 008maaau
008 201216s2020 sz s 0 eng d
020 $a 9783030439019 $q (electronic bk.)
020 $a 9783030439002 $q (paper)
024 7 $a 10.1007/978-3-030-43901-9 $2 doi
035 $a 978-3-030-43901-9
040 $a GP $c GP
041 1 $a eng $h fre
050 4 $a QA612.3 $b .H373 2020
072 7 $a PBH $2 bicssc
072 7 $a MAT022000 $2 bisacsh
072 7 $a PBH $2 thema
082 0 4 $a 514.23 $2 23
090 $a QA612.3 $b .H254 2020
100 1 $a Harari, David. $3 3459382
240 1 0 $a Cohomologie galoisienne et theorie du corps de classes. $l English.
245 1 0 $a Galois cohomology and class field theory $h [electronic resource] / $c by David Harari.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a xiv, 338 p. : $b ill., digital ; $c 24 cm.
490 1 $a Universitext, $x 0172-5939
505 0 $a Preface -- Part I Group cohomology and Galois cohomology: generalities -- 1 Cohomology of finite groups -- 2 Cohomology of cyclic groups -- 3 p-groups, the Tate-Nakayama theorem -- 4 Cohomology of profinite groups -- 5 Cohomological dimension -- 6 First notions of Galois cohomology -- Part II Local fields -- 7 Basic facts about local fields -- 8 Brauer group of a local field -- 9 Local class field theory: the reciprocity law -- 10 The Tate local duality theorem -- 11 Local class field theory: Lubin-Tate theory -- Part III Global fields -- 12 Basic facts about global fields -- 13 Cohomology of the ideles -- 14 Reciprocity law -- 15 The abelianized absolute Galois group of a global field -- Part IV Duality theorems -- 16 Class formations -- 17 Poitou-Tate duality -- 18 Some applications -- Appendix -- A Some results from homological algebra -- B A survey of analytic methods -- References -- Index.
520 $a This graduate textbook offers an introduction to modern methods in number theory. It gives a complete account of the main results of class field theory as well as the Poitou-Tate duality theorems, considered crowning achievements of modern number theory. Assuming a first graduate course in algebra and number theory, the book begins with an introduction to group and Galois cohomology. Local fields and local class field theory, including Lubin-Tate formal group laws, are covered next, followed by global class field theory and the description of abelian extensions of global fields. The final part of the book gives an accessible yet complete exposition of the Poitou-Tate duality theorems. Two appendices cover the necessary background in homological algebra and the analytic theory of Dirichlet L-series, including the Cebotarev density theorem. Based on several advanced courses given by the author, this textbook has been written for graduate students. Including complete proofs and numerous exercises, the book will also appeal to more experienced mathematicians, either as a text to learn the subject or as a reference.
650 0 $a Galois cohomology. $3 888612
650 0 $a Class field theory. $3 664678
650 1 4 $a Number Theory. $3 891078
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Universitext. $3 812115
856 4 0 $u https://doi.org/10.1007/978-3-030-43901-9
950 $a Mathematics and Statistics (Springer-11649)