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Algebraic Geometry colloquium: Purity in bad characteristics May 15, 2019 (01:30 PM PDT - 02:30 PM PDT)
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Location: MSRI: Simons Auditorium
Speaker(s) Kestutis Cesnavicius (Centre National de la Recherche Scientifique (CNRS))
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Purity phenomena in arithmetic geometry show that in sufficiently nonsingular situations finite ├ętale covers or cohomology classes extend uniquely over closed subschemes of large codimension. I will overview this in the case of the Brauer group and, more generally, in the case of fppf cohomology with finite flat group scheme coefficients. I will stress situations in which the order of the cohomology classes is not invertible on the base scheme, where a recent method is to use perfectoid techniques to reduce such questions to equal characteristic.

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