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Comparing descent obstruction and Brauer-Manin obstruction for open varieties

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 andétale Brauer-Manin obstruction for smooth pro-jective varieties is extended to smooth quasi-projective varieties, which provides the perspective to study integral points.
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Submitted on : Wednesday, July 3, 2019 - 11:27:31 AM
Last modification on : Tuesday, January 4, 2022 - 6:20:59 AM

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Yang Cao, Cyril Demarche, Fei Xu. Comparing descent obstruction and Brauer-Manin obstruction for open varieties. Transactions of the American Mathematical Society, American Mathematical Society, 2019, 371 (12), pp.8625-8650. ⟨10.1090/tran/7567⟩. ⟨hal-02171863⟩

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