Mathematical Research Letters

Volume 22 (2015)

Number 6

Integral $p$-adic Hodge theory — announcement

Pages: 1601 – 1612



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)


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.

Accepted 15 September 2015

Published 23 May 2016