Torsors and rational points

By:

Skorobogatov, Alexei

Series: Cambridge tracts in mathematics, no. 144Publication details: Cambridge University Press, 2001. Cambridge:Description: vii, 186p.; hbk; 24cmISBN:

9780521802376

Subject(s):

DDC classification:

512.4 SKO

Summary: 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. https://www.cambridge.org/core/books/torsors-and-rational-points/76C9B8890C39601665082CFA8258E20E#fndtn-information

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Holdings
Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	IIT Gandhinagar	General	512.4 SKO (Browse shelf(Opens below))	1	Available		031770

Includes index and references

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.

https://www.cambridge.org/core/books/torsors-and-rational-points/76C9B8890C39601665082CFA8258E20E#fndtn-information

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