Descent theory for open varieties

Details Descent theory for open varieties Descent theory for open varieties

2010-12-08

arxiv.org/abs/1012.1765v1

Mathematics

Algebraic Geometry

28 pages

Scientific paper

We extend the descent theory of Colliot-Th\'el\`ene and Sansuc to arbitrary
smooth algebraic varieties by removing the condition that every invertible
regular function is constant. This links the Brauer--Manin obstruction for
integral points on arithmetic schemes to the obstructions defined by torsors
under groups of multiplicative type.

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