Comparing descent obstruction and Brauer-Manin obstruction for open varieties
Résumé
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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