Torsors and rational points:
The classical descent on curves of genus one can be interpreted as providing conditions on the set of rational points of an algebraic variety X defined over a number field, viewed as a subset of its adelic points. This is the natural set-up of the Hasse principle and various approximation properties...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2001
|
| Series: | Cambridge tracts in mathematics
144 |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBR01 Volltext |
| Summary: | The classical descent on curves of genus one can be interpreted as providing conditions on the set of rational points of an algebraic variety X defined over a number field, viewed as a subset of its adelic points. This is the natural set-up of the Hasse principle and various approximation properties of rational points. The most famous among such conditions is the Manin obstruction exploiting the Brauer-Grothendieck group of X. It emerged recently that a non-abelian generalization of descent sometimes provides stronger conditions on rational points. An all-encompassing 'obstruction' is related to the X-torsors (families of principal homogenous spaces with base X) under algebraic groups. This book, first published in 2001, is a detailed exposition of the general theory of torsors with key examples, the relation of descent to the Manin obstruction, and applications of descent: to conic bundles, to bielliptic surfaces, and to homogenous spaces of algebraic groups |
| Physical Description: | 1 Online-Ressource (viii, 187 Seiten) |
| ISBN: | 9780511549588 |
| DOI: | 10.1017/CBO9780511549588 |
Staff View
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| 520 | |a The classical descent on curves of genus one can be interpreted as providing conditions on the set of rational points of an algebraic variety X defined over a number field, viewed as a subset of its adelic points. This is the natural set-up of the Hasse principle and various approximation properties of rational points. The most famous among such conditions is the Manin obstruction exploiting the Brauer-Grothendieck group of X. It emerged recently that a non-abelian generalization of descent sometimes provides stronger conditions on rational points. An all-encompassing 'obstruction' is related to the X-torsors (families of principal homogenous spaces with base X) under algebraic groups. This book, first published in 2001, is a detailed exposition of the general theory of torsors with key examples, the relation of descent to the Manin obstruction, and applications of descent: to conic bundles, to bielliptic surfaces, and to homogenous spaces of algebraic groups | ||
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Record in the Search Index
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| author | Skorobogatov, Alexei 1961- |
| author_GND | (DE-588)172377021 |
| author_facet | Skorobogatov, Alexei 1961- |
| author_role | aut |
| author_sort | Skorobogatov, Alexei 1961- |
| author_variant | a s as |
| building | Verbundindex |
| bvnumber | BV043942045 |
| classification_rvk | SK 240 |
| collection | ZDB-20-CBO |
| contents | Torsors Torsors: general theory Examples of torsors Descent and manin obstruction Obstructions over number fields Abelian descent and manin obstruction |
| ctrlnum | (ZDB-20-CBO)CR9780511549588 (OCoLC)849888141 (DE-599)BVBBV043942045 |
| dewey-full | 512/.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.4 |
| dewey-search | 512/.4 |
| dewey-sort | 3512 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511549588 |
| format | Electronic eBook |
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| id | DE-604.BV043942045 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511549588 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351015 |
| oclc_num | 849888141 |
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| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (viii, 187 Seiten) |
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| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Cambridge University Press |
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| spelling | Skorobogatov, Alexei 1961- Verfasser (DE-588)172377021 aut Torsors and rational points Alexei Skorobogatov Torsors & Rational Points Cambridge Cambridge University Press 2001 1 Online-Ressource (viii, 187 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 144 Torsors Torsors: general theory Examples of torsors Descent and manin obstruction Obstructions over number fields Abelian descent and manin obstruction The classical descent on curves of genus one can be interpreted as providing conditions on the set of rational points of an algebraic variety X defined over a number field, viewed as a subset of its adelic points. This is the natural set-up of the Hasse principle and various approximation properties of rational points. The most famous among such conditions is the Manin obstruction exploiting the Brauer-Grothendieck group of X. It emerged recently that a non-abelian generalization of descent sometimes provides stronger conditions on rational points. An all-encompassing 'obstruction' is related to the X-torsors (families of principal homogenous spaces with base X) under algebraic groups. This book, first published in 2001, is a detailed exposition of the general theory of torsors with key examples, the relation of descent to the Manin obstruction, and applications of descent: to conic bundles, to bielliptic surfaces, and to homogenous spaces of algebraic groups Torsion theory (Algebra) Rational points (Geometry) Torsionstheorie (DE-588)4451084-6 gnd rswk-swf Torsionstheorie (DE-588)4451084-6 s DE-604 Erscheint auch als Druck-Ausgabe 978-0-521-80237-6 https://doi.org/10.1017/CBO9780511549588 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Skorobogatov, Alexei 1961- Torsors and rational points Torsors Torsors: general theory Examples of torsors Descent and manin obstruction Obstructions over number fields Abelian descent and manin obstruction Torsion theory (Algebra) Rational points (Geometry) Torsionstheorie (DE-588)4451084-6 gnd |
| subject_GND | (DE-588)4451084-6 |
| title | Torsors and rational points |
| title_alt | Torsors & Rational Points Torsors Torsors: general theory Examples of torsors Descent and manin obstruction Obstructions over number fields Abelian descent and manin obstruction |
| 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 theory (Algebra) Rational points (Geometry) Torsionstheorie (DE-588)4451084-6 gnd |
| topic_facet | Torsion theory (Algebra) Rational points (Geometry) Torsionstheorie |
| url | https://doi.org/10.1017/CBO9780511549588 |
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