Torsors and Rational Points

By Alexei N. Skorobogatov. 2001

380 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d34ade8e470ac092a19bae97bc47833ff0eb3fdb

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Citations in the corpus

The Brauer-Manin obstruction for subvarieties of abelian varieties over function fields (2006, methodology): “See also [ Sko01 ,Fly04,Poo05,Sto06]: the last of these in particular contains many conjectures and theorems relating descent information, the method of Chabauty and Coleman, the Brauer-Manin obstruction, and Grothendieck’s section conjecture.”
Twists of X(7) and primitive solutions to x^2+y^3=z^7 (2005, background): “Descent theory (cf. [Chevalley-Weil1930] and [Skorobogatov2001, §5.3]) tells us the following: • The set of classes in the Galois cohomology set H1(Q, G) that are unramified outside 2, 3, and 7 is finite.”
Igusa integrals and volume asymptotics in analytic and adelic geometry (2009, background): “Such torsors have been successfully applied to the study of rational points on the variety V (Hasse principle, weak approximation, counting of rational points of bounded height); see [18, 40, 9, 46].”
Singular Localization and Intertwining Functors for Reductive Lie Algebras in Prime Characteristic (2006, background): “DP. A reader unfamiliar with torsors should consult [ Sk ].”
Insufficiency of the Brauer-Manin obstruction applied to étale covers (2008, background): “(See [ Sko01 , §5.3].) If G is a (not necessarily connected) linear algebraic group over k, and f : Y ! X is a right torsor under G, then any 1-cocycle 2 Z1(k,G) gives rise to a “twisted” right torsor f : Y ! X under a twisted form G of”
Brauer–Manin obstruction for integral points of homogeneous spaces and representation by integral quadratic forms (2007, methodology): “For background on the Brauer–Manin obstruction, we refer the reader to [38] and the literature cited there.”
Arithmetic duality theorems for 1-motives (2003, background): “(This question was raised by Skorobogatov in [26], p.”
Manin obstruction to strong approximation for homogeneous spaces (2009, neutral): “1, or [40], Section 5.”
On the Arithmetic of Del Pezzo Surfaces of Degree 2 (2004, background): “In fact the same is true for weak approximation; see [16].”
MINIMISATION AND REDUCTION OF 2-, 3- AND 4-COVERINGS OF ELLIPTIC CURVES (2009, background): “In [ Sk , §8.1], an example is given of a 4-covering C of the elliptic curve E : y2 = x3 i 1221 that represents”