Galois groups and fundamental groups:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge Univ. Press
2009
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge studies in advanced mathematics
117 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018611423&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke Includes bibliographical references and index |
| Umfang: | IX, 270 S. |
| ISBN: | 9780521888509 |
Internformat
MARC
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| 245 | 1 | 0 | |a Galois groups and fundamental groups |c Tamás Szamuely |
| 250 | |a 1. publ. | ||
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| 300 | |a IX, 270 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Galois theory | |
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| 830 | 0 | |a Cambridge studies in advanced mathematics |v 117 |w (DE-604)BV000003678 |9 117 | |
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Datensatz im Suchindex
| _version_ | 1819297134053163008 |
|---|---|
| adam_text | Contents
Preface
page vii
1
Galois theory of fields
1
1.1
Algebraic field extensions
1
1.2
Galois extensions
4
1.3
Infinite Galois extensions
9
1.4
Interlude on category theory
15
1.5
Finite
étale
algebras
20
2
Fundamental groups in topology
27
2.1
Covers
27
2.2
Galois covers
30
2.3
The monodromy action
34
2.4
The universal cover
39
2.5
Locally constant sheaves and their classification
45
2.6
Local systems
51
2.7
The Riemann-Hilbert correspondence
54
3
Riemann surfaces
65
3.1
Basic concepts
65
3.2
Local structure of holomorphic maps
67
3.3
Relation with field theory
72
3.4
The absolute Galois group of C(f
) 78
3.5
An alternate approach: patching Galois covers
83
3.6
Topology of Riemann surfaces
86
4
Fundamental groups of algebraic curves
93
4.1
Background in commutative algebra
93
4.2
Curves over an algebraically closed field
99
4.3
Affine
curves over a general base field
105
4.4
Proper normal curves
110
4.5
Finite branched covers of normal curves 1
14
4.6
The algebraic fundamental group
119
4.7
The outer Galois action
123
4.8
Application to the inverse Galois problem
129
4.9
A survey of advanced results
134
vi
Contents
5 Fundamental
groups of schemes
142
5.1
The vocabulary of schemes
142
5.2
Finite
étale
covers of schemes
152
5.3
Galois theory for finite
étale
covers
159
5.4
The algebraic fundamental group in the general case
166
5.5
First properties of the fundamental group
170
5.6
The homotopy exact sequence and applications
175
5.7
Structure theorems for the fundamental group
182
5.8
The abelianized fundamental group
193
6
Tannakian fundamental groups
206
6.1
Affine
group schemes and
Hopf
algebras
206
6.2
Categories of comodules
214
6.3
Tensor categories and the Tannaka-Krein theorem
222
6.4
Second interlude on category theory
228
6.5
Neutral Tannakian categories
232
6.6
Differential Galois groups
242
6.7
Nori s fundamental group scheme
248
Bibliography
261
Index
268
|
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| discipline | Mathematik |
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| id | DE-604.BV035751374 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T13:59:21Z |
| institution | BVB |
| isbn | 9780521888509 |
| language | English |
| lccn | 2009003670 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018611423 |
| oclc_num | 297147099 |
| open_access_boolean | |
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| owner_facet | DE-20 DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-11 DE-384 DE-703 DE-188 |
| physical | IX, 270 S. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spellingShingle | Szamuely, Tamás Galois groups and fundamental groups Cambridge studies in advanced mathematics Galois theory Gruppentheorie (DE-588)4072157-7 gnd Galois-Theorie (DE-588)4155901-0 gnd |
| subject_GND | (DE-588)4072157-7 (DE-588)4155901-0 |
| title | Galois groups and fundamental groups |
| title_auth | Galois groups and fundamental groups |
| title_exact_search | Galois groups and fundamental groups |
| title_full | Galois groups and fundamental groups Tamás Szamuely |
| title_fullStr | Galois groups and fundamental groups Tamás Szamuely |
| title_full_unstemmed | Galois groups and fundamental groups Tamás Szamuely |
| title_short | Galois groups and fundamental groups |
| title_sort | galois groups and fundamental groups |
| topic | Galois theory Gruppentheorie (DE-588)4072157-7 gnd Galois-Theorie (DE-588)4155901-0 gnd |
| topic_facet | Galois theory Gruppentheorie Galois-Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018611423&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003678 |
| work_keys_str_mv | AT szamuelytamas galoisgroupsandfundamentalgroups |