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. |
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Main Author: | |
Language: | English |
Published: |
Cambridge :
Cambridge University Press,
2001.
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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 |
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. |
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Note: | Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
Call Number: | QA251.3 .S62 2001 |
ISBN: | 9780511549588 (ebook) |
DOI: | 10.1017/CBO9780511549588 |