Comparing descent obstruction and Brauer-Manin obstruction for open varieties

Cao, Yang; Demarche, Cyril; Xu, Fei

doi:10.1090/tran/7567

Comparing descent obstruction and Brauer-Manin obstruction for open varieties
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by Yang Cao, Cyril Demarche and Fei Xu PDF

Trans. Amer. Math. Soc. 371 (2019), 8625-8650 Request permission

Abstract:

We provide a relation between Brauer-Manin obstruction and descent obstruction for torsors over not necessarily proper varieties under a connected linear algebraic group or a group of multiplicative type. Such a relation is also refined for torsors under a torus. The equivalence between descent obstruction and étale Brauer-Manin obstruction for smooth projective varieties is extended to smooth quasi-projective varieties, which provides the perspective to study integral points.

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