Torsors and rational points / Alexei Skorobogatov.
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...
| Uniform Title: | Cambridge tracts in mathematics ;
144. |
|---|---|
| Main Author: | |
| Language: | English |
| Published: |
Cambridge :
Cambridge University Press,
2001.
|
| Series: | Cambridge tracts in mathematics ;
144. |
| Subjects: | |
| Online Access: | |
| Physical Description: | 1 online resource (viii, 187 pages) : digital, PDF file(s). |
| Variant Title: |
Torsors & Rational Points. |
| Format: | Electronic eBook |
MARC
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| 100 | 1 | |a Skorobogatov, Alexei, |d 1961- |e author. |0 http://id.loc.gov/authorities/names/n2001006709 | |
| 245 | 1 | 0 | |a Torsors and rational points / |c Alexei Skorobogatov. |
| 246 | 3 | |a Torsors & Rational Points. | |
| 264 | 1 | |a Cambridge : |b Cambridge University Press, |c 2001. | |
| 300 | |a 1 online resource (viii, 187 pages) : |b digital, PDF file(s). | ||
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| 490 | 1 | |a Cambridge tracts in mathematics ; |v 144 | |
| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015). | ||
| 505 | 0 | 0 | |t Torsors -- |t Torsors: general theory -- |t Examples of torsors -- |t Descent and manin obstruction -- |t Obstructions over number fields -- |t Abelian descent and manin obstruction. |
| 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. | ||
| 650 | 0 | |a Torsion theory (Algebra) |0 http://id.loc.gov/authorities/subjects/sh85136153 | |
| 650 | 0 | |a Rational points (Geometry) |0 http://id.loc.gov/authorities/subjects/sh2001008362 | |
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| 830 | 0 | |a Cambridge tracts in mathematics ; |v 144. |0 http://id.loc.gov/authorities/names/n42005726 | |
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