An introduction to Galois cohomology and its applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a]
Cambridge Univ. Press
2010
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | London Mathematical Society lecture note series
377 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 315 S. graph. Darst. |
| ISBN: | 9780521738668 0521738660 |
Internformat
MARC
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| 100 | 1 | |a Berhuy, Grégory |d 1973- |e Verfasser |0 (DE-588)142057878 |4 aut | |
| 245 | 1 | 0 | |a An introduction to Galois cohomology and its applications |c Grégory Berhuy |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a] |b Cambridge Univ. Press |c 2010 | |
| 300 | |a XI, 315 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a London Mathematical Society lecture note series |v 377 | |
| 650 | 0 | 7 | |a Galois-Kohomologie |0 (DE-588)4019172-2 |2 gnd |9 rswk-swf |
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| 830 | 0 | |a London Mathematical Society lecture note series |v 377 |w (DE-604)BV000000130 |9 377 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-020535080 | ||
Datensatz im Suchindex
| _version_ | 1804143222131261440 |
|---|---|
| adam_text | Contents
I.I
Reminiscences on field
theory
1.2
Gaiois theory
1.2.1
Definitions
and first examples
1.2.2
The Galois
correspondence
1.2.3
Morphisms
of Galois extensions
1.2.4
The Galois
group as
a profinite
group
Exercises
Foreword
ряде
xi
Introduction
1
Part I An introduction to Galois cohomology
11
I Infinite Galois theory
13
13
17
17
18
19
21
24
II Cohomology of
profinite
groups
26
11.3 Cohomology sets: basic properties
26
11.3.1 Definitions
26
11.3.2 Functoriality
36
11.
3.3
Cohomology sets as a direct limit
41
11.4 Cohomology sequences
45
11.4.1 The case of a subgroup
46
11.
4.2
The case of a normal subgroup
51
11.4.3 The case of a central subgroup
52
11.5 Twisting
56
11.6 Cup-products
61
Exercises
64
III Galois cohomology
69
III.7 Warm-up
69
Ш.7.1
Digression: categories and functors
69
vii
viii Contents
III.
7.2
Algebraic group-schemes
77
ΠΙ.7.3
The Galois cohomology functor
85
111.
8
Abstract Galois descent
96
111.
8.1
Matrices reloaded
97
111.
8.2
Actions of group-valued functors
99
111.8.3 Twisted forms
101
111.8.4 The Galois descent condition
103
111.8.5 Stabilizers
104
111.8.6 Galois descent lemma
106
111.8.7 Hilbert s Theorem
90 110
111.9 First applications of Galois descent
117
III.
9.1
Galois descent of algebras
117
IIL9.2 The conjugacy problem
121
III.9.3 Cup-products with values in
Џ2
126
Exercises
130
IV Galois cohomology of quadratic forms
134
IV.
10
Algebraic group-schemes associated to quadratic forms
134
IV.
10.1
Quadratic forms over rings
134
IV.10.2 Orthogonal groups
136
IV.
10.3
Clifford groups and spinors
139
IV.
11
Galois cohomology of quadratic forms
145
I V.I
1.1
Galois cohomology of orthogonal groups
145
IV.
11.2
Galois cohomology of spinors
147
IV.
12
Cohomological invariants of quadratic forms
152
IV.
12.1
Classification of quadratic forms over
Q
152
IV.12.2 Higher cohomological invariants
154
Exercises
158
V
Étale
and Galois algebras
160
V.13
Étale
algebras
160
V.14 Galois algebras
164
V.14.1 Definition and first properties
164
V.14.2 Galois algebras and Galois cohomology
170
Exercises
177
VI Group extensions, Galois embedding problems and Galois
cohomology
179
VI.
15
Group extensions
179
VI.
16
Galois embedding problems
185
Exercises
187
Part II Applications
189
VII
Galois embedding problems and the trace form
191
VIL17 The trace form of an
étale
algebra W2
Contents ix
VII.18
Computation of
e* (sn)
196
VII.
19
Applications to inverse Galois theory
200
Exercises
205
VIII
Galois cohomology of central simple algebras
207
VIII.20 Central simple algebras
207
VIII.21 Algebras with involutions
217
VIII.21.1 Basic concepts
217
VIII.21.2 Hyperbolic involutions
222
VIII.21.3 Similitudes
226
VIII.21.4
Cohomology of algebras with involution
228
VIII.21.
5
Trace forms
231
Exercises
245
IX Digression: a geometric interpretation of Hl(—,G)
249
IX.
22
Reminiscences on schemes
249
IX.23
Torsors
253
Exercises
259
X Galois cohomology and Noether s problem
261
X.24 Formulation of Noether s problem
261
X.25 The strategy
262
X.26 Residue maps
265
X.27 An unramified
cohomołogical
invariant
271
X.28 Proof of Theorem X.24.1
272
XI The rationality problem for adjoint algebraic groups
274
XI.29
Д
-equivalence
groups
275
XI.
30
The rationality problem for adjoint groups
278
XI.31 Examples of non-rational adjoint groups
281
Exercises
287
XII
Essential dimension of functors
290
XII.32 Essential dimension: definition and first examples
290
XII.33 First results
292
XII.34
Cohomołogical
invariants and essential dimension
296
XII.35
Generic objects and essential dimension
298
XII.36 Generically free representations
300
XII.37 Some examples
301
XII.38 Complements and open problems
306
Exercises
308
References
310
Index
314
|
| any_adam_object | 1 |
| author | Berhuy, Grégory 1973- |
| author_GND | (DE-588)142057878 |
| author_facet | Berhuy, Grégory 1973- |
| author_role | aut |
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| bvnumber | BV036614920 |
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| dewey-full | 514.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.23 |
| dewey-search | 514.23 |
| dewey-sort | 3514.23 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV036614920 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:44:14Z |
| institution | BVB |
| isbn | 9780521738668 0521738660 |
| language | English |
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| physical | XI, 315 S. graph. Darst. |
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| series | London Mathematical Society lecture note series |
| series2 | London Mathematical Society lecture note series |
| spelling | Berhuy, Grégory 1973- Verfasser (DE-588)142057878 aut An introduction to Galois cohomology and its applications Grégory Berhuy 1. publ. Cambridge [u.a] Cambridge Univ. Press 2010 XI, 315 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society lecture note series 377 Galois-Kohomologie (DE-588)4019172-2 gnd rswk-swf Galois-Kohomologie (DE-588)4019172-2 s DE-604 London Mathematical Society lecture note series 377 (DE-604)BV000000130 377 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020535080&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Berhuy, Grégory 1973- An introduction to Galois cohomology and its applications London Mathematical Society lecture note series Galois-Kohomologie (DE-588)4019172-2 gnd |
| subject_GND | (DE-588)4019172-2 |
| title | An introduction to Galois cohomology and its applications |
| title_auth | An introduction to Galois cohomology and its applications |
| title_exact_search | An introduction to Galois cohomology and its applications |
| title_full | An introduction to Galois cohomology and its applications Grégory Berhuy |
| title_fullStr | An introduction to Galois cohomology and its applications Grégory Berhuy |
| title_full_unstemmed | An introduction to Galois cohomology and its applications Grégory Berhuy |
| title_short | An introduction to Galois cohomology and its applications |
| title_sort | an introduction to galois cohomology and its applications |
| topic | Galois-Kohomologie (DE-588)4019172-2 gnd |
| topic_facet | Galois-Kohomologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020535080&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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