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Torsors and rational points

Skorobogatov, Alexei, (1961-)

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Torsors and rational points

Record Type:	Electronic resources : Monograph/item
Title/Author:	Torsors and rational points/ Alexei Skorobogatov.
remainder title:	Torsors & Rational Points
Author:	Skorobogatov, Alexei,
Published:	Cambridge :Cambridge University Press, : 2001.,
Description:	viii, 187 p. :ill., digital ;24 cm.
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Subject:	Torsion theory (Algebra) -
Online resource:	https://doi.org/10.1017/CBO9780511549588
ISBN:	9780511549588

Torsors and rational points
Skorobogatov, Alexei,1961-

Torsors and rational points[electronic resource] /Torsors & Rational PointsAlexei Skorobogatov. - Cambridge :Cambridge University Press,2001. - viii, 187 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;144. - Cambridge tracts in mathematics ;144..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Torsors --

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.

ISBN: 9780511549588Subjects--Topical Terms:

711381
Torsion theory (Algebra)

LC Class. No.: QA251.3 / .S62 2001

Dewey Class. No.: 512.4

Torsors and rational points
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245 1 0 $a Torsors and rational points $h [electronic resource] / $c Alexei Skorobogatov.
246 3 $a Torsors & Rational Points
260 $a Cambridge : $b Cambridge University Press, $c 2001.
300 $a viii, 187 p. : $b ill., digital ; $c 24 cm.
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) $3 711381
650 0 $a Rational points (Geometry) $3 811921
830 0 $a Cambridge tracts in mathematics ; $v 144. $3 3470491
856 4 0 $u https://doi.org/10.1017/CBO9780511549588