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2021 Integral p-adic Hodge theory of formal schemes in low ramification
Yu Min
Algebra Number Theory 15(4): 1043-1076 (2021). DOI: 10.2140/ant.2021.15.1043

Abstract

We prove that for any proper smooth formal scheme 𝔛 over 𝒪K, where 𝒪K is the ring of integers in a complete discretely valued nonarchimedean extension K of 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 ie<p1. Thanks to the comparison theorems in the recent works of Bhatt, Morrow and Scholze (2018, 2019), we can then get an integral comparison theorem for formal schemes when the cohomological degree i satisfies ie<p1, which generalizes the case of schemes under the condition (i+1)e<p1 proven by Fontaine and Messing (1987) and Caruso (2008).

Citation

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Yu Min. "Integral p-adic Hodge theory of formal schemes in low ramification." Algebra Number Theory 15 (4) 1043 - 1076, 2021. https://doi.org/10.2140/ant.2021.15.1043

Information

Received: 11 April 2020; Revised: 16 September 2020; Accepted: 17 October 2020; Published: 2021
First available in Project Euclid: 25 June 2021

Digital Object Identifier: 10.2140/ant.2021.15.1043

Subjects:
Primary: 14F30

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.15 • No. 4 • 2021
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