TORSORS AND RATIONAL POINTS by Skorobogatov, A ISBN 0521802377
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[edit] TORSORS AND RATIONAL POINTS
Complete and coherent exposition of the theory and applications of torsors to rational points.
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 represents the first detailed exposition of 1) the general theory of torsors with key examples, 2) the relation of descent to the Manin obstruction, and 3) applications of descent: to conic bundles, to bielliptic surfaces, and to homogenous spaces of algebraic groups.
[edit] Book Details
[edit] Title
TORSORS AND RATIONAL POINTS
[edit] Author
Skorobogatov, A
[edit] ISBN
0521802377
[edit] Published
05/07/2001
[edit] Publisher
Cambridge University Press
[edit] Binding
hardback
[edit] Retail Price
42 (GBP)
[edit] Typical Price Online
41.16 (GBP)
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