Torsors and rational points:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
2001
|
| Edition: | 1. publ. |
| Series: | Cambridge tracts in mathematics
144 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 187 S. |
| ISBN: | 0521802377 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
1 Introduction page 1
Part one: TORSORS 7
2 Torsors: general theory 11
2.1 Torsors over a field 11
2.2 Torsors and Cech cohomology 13
2.3 Torsors under groups of multiplicative type 24
2.4 Obstructions to existence of rational points over arbitrary fields 34
3 Examples of torsors 42
3.1 Torsors in geometric invariant theory 42
Appendix. Classification of Del Pezzo surfaces of degree 5 44
3.2 Homogeneous spaces and central extensions 49
3.3 Torsors under abelian varieties 54
Appendix. Equations for 2 and 4 coverings of elliptic curves 58
4 Abelian torsors 62
4.1 From abelian torsors to Azumaya algebras 62
4.2 A commutative diagram 68
4.3 Local description of abelian torsors 72
4.4 Torsors associated with a dominant morphism to P 79
Part two: DESCENT AND MANIN OBSTRUCTION 95
5 Obstructions over number fields 98
5.1 The Hasse principle, weak and strong approximation 98
5.2 The Manin obstruction 101
5.3 Descent obstructions 104
6 Abelian descent and Manin obstruction 112
6.1 Descent theory 113
vii
viii Contents
6.2 Manin obstruction and global duality pairings 121
6.3 Compactifications of torsors under tori 130
7 Abelian descent on conic bundle surfaces 134
7.1 Brauer group of conic bundles 135
7.2 Chatelet surfaces 139
7.3 Some intersections of two quadrics in P| 146
7.4 Conic bundles with six singular fibres 148
8 Non abelian descent on bielliptic surfaces 157
8.1 Beyond the Manin obstruction 158
Appendix. An example of 4 torsion in U1(E) 163
8.2 Interpretation in terms of non abelian torsors 164
9 Homogeneous spaces and non abelian cohomology 168
9.1 Liens and non abelian H2 168
9.2 The Springer class of a homogeneous space 172
9.3 Abelianization of non abelian H2 173
9.4 Hasse principle for non abelian H2 174
9.5 Descent on homogeneous spaces 175
References 179
Index 187
|
| any_adam_object | 1 |
| author | Skorobogatov, Alexei |
| author_facet | Skorobogatov, Alexei |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV013859977 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:53:18Z |
| institution | BVB |
| isbn | 0521802377 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009479435 |
| oclc_num | 46359545 |
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| physical | VIII, 187 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Skorobogatov, Alexei Verfasser aut Torsors and rational points Alexei Skorobogatov 1. publ. Cambridge Cambridge Univ. Press 2001 VIII, 187 S. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 144 Torsion, Théorie de la (Algèbre) Rational points (Geometry) Torsion theory (Algebra) Torsionstheorie (DE-588)4451084-6 gnd rswk-swf Torsionstheorie (DE-588)4451084-6 s DE-604 Cambridge tracts in mathematics 144 (DE-604)BV000000001 144 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009479435&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Skorobogatov, Alexei Torsors and rational points Cambridge tracts in mathematics Torsion, Théorie de la (Algèbre) Rational points (Geometry) Torsion theory (Algebra) Torsionstheorie (DE-588)4451084-6 gnd |
| subject_GND | (DE-588)4451084-6 |
| title | Torsors and rational points |
| title_auth | Torsors and rational points |
| title_exact_search | Torsors and rational points |
| title_full | Torsors and rational points Alexei Skorobogatov |
| title_fullStr | Torsors and rational points Alexei Skorobogatov |
| title_full_unstemmed | Torsors and rational points Alexei Skorobogatov |
| title_short | Torsors and rational points |
| title_sort | torsors and rational points |
| topic | Torsion, Théorie de la (Algèbre) Rational points (Geometry) Torsion theory (Algebra) Torsionstheorie (DE-588)4451084-6 gnd |
| topic_facet | Torsion, Théorie de la (Algèbre) Rational points (Geometry) Torsion theory (Algebra) Torsionstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009479435&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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