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arXiv · 1012.1765

Descent theory for open varieties

David Harari·Alexei N. Skorobogatov
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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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David Harari, Alexei N. Skorobogatov. 2010-12-08. Descent theory for open varieties. https://arxiv.org/abs/1012.1765

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