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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 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.
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Cambridge University Press; July 2001
197 pages; ISBN 9780511891649
Read online, or download in secure PDF format
197 pages; ISBN 9780511891649
Read online, or download in secure PDF format
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0511891644
9780511891649
9780521802376