Integral $p$-adic Hodge theory - announcement

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 \'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.