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Torsors and rational points

Skorobogatov, Alexei, (1961-)

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Torsors and rational points

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Torsors and rational points/ Alexei Skorobogatov.
其他題名:	Torsors & Rational Points
作者:	Skorobogatov, Alexei,
出版者:	Cambridge :Cambridge University Press, : 2001.,
面頁冊數:	viii, 187 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Torsion theory (Algebra) -
電子資源:	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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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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