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...

Ausführliche Beschreibung

Bibliographische Detailangaben

1. Verfasser:	Skorobogatov, Alexei 1961- (VerfasserIn)
Format:	Elektronisch E-Book
Sprache:	English
Veröffentlicht:	Cambridge Cambridge University Press 2001
Schriftenreihe:	Cambridge tracts in mathematics 144
Schlagworte:	Torsion theory (Algebra) Rational points (Geometry) Torsionstheorie
Online-Zugang:	BSB01 FHN01 UBR01 Volltext
Zusammenfassung:	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
Beschreibung:	1 Online-Ressource (viii, 187 Seiten)
ISBN:	9780511549588
DOI:	10.1017/CBO9780511549588