Descent theory for open varieties

Published 8 Dec 2010 in math.AG and math.NT | (1012.1765v1)

Abstract: 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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