Integral $p$-adic Hodge theory - announcement

Bhargav Bhatt; Matthew Morrow; Peter Scholze

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arXiv · 1507.08129

Integral $p$-adic Hodge theory - announcement

Bhargav Bhatt·Matthew Morrow·Peter Scholze

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Abstract

Given a proper, smooth (formal) scheme over the ring of integers of $\mathbb C_p$, we prove that if the crystalline cohomology of its special fibre is torsion-free then the $p$-adic étale cohomology of its generic fibre is also torsion-free. In this announcement we sketch the proof, which relies on the construction of a new cohomology theory interpolating between crystalline and étale cohomology. Further details and results, including a comparison isomorphism, will be presented in the full forthcoming article.

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Bhargav Bhatt, Matthew Morrow, Peter Scholze. 2015-07-29. Integral $p$-adic Hodge theory - announcement. https://arxiv.org/abs/1507.08129

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