Integral $p$-adic Hodge theory - announcement
Algebraic Geometry
2015-07-30 v1 Number Theory
Abstract
Given a proper, smooth (formal) scheme over the ring of integers of , we prove that if the crystalline cohomology of its special fibre is torsion-free then the -adic \'etale 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 \'etale cohomology. Further details and results, including a comparison isomorphism, will be presented in the full forthcoming article.
Cite
@article{arxiv.1507.08129,
title = {Integral $p$-adic Hodge theory - announcement},
author = {Bhargav Bhatt and Matthew Morrow and Peter Scholze},
journal= {arXiv preprint arXiv:1507.08129},
year = {2015}
}