Integral p-adic Hodge theory - announcement

2015/07/29 by Bhatt, Bhargav, Morrow, Matthew, Scholze, Peter
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1507.08129

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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