000			01767 a2200229 4500
008			220820b |||||||| |||| 00| 0 eng d
020			_a9780521802376
082			_a512.4 _bSKO
100			_aSkorobogatov, Alexei
245			_aTorsors and rational points
260			_bCambridge University Press, _c2001. _aCambridge:
300			_avii, 186p.; _bhbk; _c24cm.
440			_aCambridge tracts in mathematics, no. 144
504			_aIncludes index and references
520			_aThe 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. https://www.cambridge.org/core/books/torsors-and-rational-points/76C9B8890C39601665082CFA8258E20E#fndtn-information
650			_aTorsion theory--Algebra
650			_aRational points--Geometry
650			_aReal and complex analysis
650			_aNumber theory
650			_aX-torsors
942			_2ddc _cTD
999			_c56676 _d56676