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arXiv · 1606.01463

Specializing varieties and their cohomology from characteristic $0$ to characteristic $p$

Bhargav Bhatt
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Abstract

We present a semicontinuity result, proven in recent joint work with Morrow and Scholze, relating the mod $p$ singular cohomology of a smooth projective complex algebraic variety X to the de Rham cohomology of a smooth characteristic $p$ specialization of X: the rank of the former is bounded above by that of the latter. The path to this result passes through $p$-adic Hodge theory and perfectoid geometry, so we survey the relevant aspects of those subjects as well.

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Bhargav Bhatt. 2016-06-05. Specializing varieties and their cohomology from characteristic $0$ to characteristic $p$. https://arxiv.org/abs/1606.01463

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