Integral \(p\)-adic Hodge theory

DOI10.1007/S10240-019-00102-ZzbMATH Open1446.14011arXiv1602.03148OpenAlexW2963305697MaRDI QIDQ1720273

Author name not available (Why is that?)

Publication date: 8 February 2019

Published in: (Search for Journal in Brave)

Abstract: We construct a new cohomology theory for proper smooth (formal) schemes over the ring of integers of C_p. It takes values in a mixed-characteristic analogue of Dieudonne modules, which was previously defined by Fargues as a version of Breuil-Kisin modules. Notably, this cohomology theory specializes to all other known p-adic cohomology theories, such as crystalline, de Rham and etale cohomology, which allows us to prove strong integral comparison theorems. The construction of the cohomology theory relies on Faltings's almost purity theorem, along with a certain functor $Leta$ on the derived category, defined previously by Berthelot-Ogus. On affine pieces, our cohomology theory admits a relation to the theory of de Rham-Witt complexes of Langer-Zink, and can be computed as a q-deformation of de Rham cohomology.

Full work available at URL: https://arxiv.org/abs/1602.03148

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: Integral \(p\)-adic Hodge theory

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q1720273)