Integral $p$-adic Hodge theory — announcement

Abstract

Given a proper, smooth (formal) scheme over the ring of integers of 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.

Locations

• Mathematical Research Letters - View - PDF
• arXiv (Cornell University) - View - PDF