Integral \(p\)-adic Hodge theory of formal schemes in low ramification

DOI10.2140/ANT.2021.15.1043zbMATH Open1478.14041arXiv2004.04436OpenAlexW3016041440MaRDI QIDQ2036842

Author name not available (Why is that?)

Publication date: 30 June 2021

Published in: (Search for Journal in Brave)

Abstract: We prove that for any proper smooth formal scheme

f r a k X

over

m a t h c a l O_{K}

, where

m a t h c a l O_{K}

is the ring of integers in a complete discretely valued nonarchimedean extension

K

of

m a t h b b Q_{p}

with perfect residue field

k

and ramification degree

e

, the

i

-th Breuil-Kisin cohomology group and its Hodge-Tate specialization admit nice decompositions when

i e < p - 1

. Thanks to the comparison theorems in the recent works of Bhatt, Morrow and Scholze, we can then get an integral comparison theorem for formal schemes when the cohomological degree

i

satisfies

i e < p - 1

, which generalizes the case of schemes under the condition

(i + 1) e < p - 1

proven by Fontaine-Messing and Caruso.

Full work available at URL: https://arxiv.org/abs/2004.04436

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