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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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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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https://doi.org/10.1017/CBO9780511549588
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W9396629
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11.線上閱覽_V
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EB QA251.3 .S62 2001
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