Mathematical Research Letters

Volume 22 (2015)

Number 6

Integral $p$-adic Hodge theory — announcement

Pages: 1601 – 1612

DOI: https://dx.doi.org/10.4310/MRL.2015.v22.n6.a3

Authors

B. Bhatt (Department of Mathematics, University of Michigan, Ann Arbor, Mich., U.S.A.)

M. Morrow (Mathematisches Institut, Universität Bonn, Germany)

P. Scholze (Mathematisches Institut, Universität Bonn, Germany)

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 crystalline and étale cohomology. Further details and results will be presented in the full forthcoming article.

Full Text (PDF format)

Accepted 15 September 2015

Published 23 May 2016