Abstract
We prove that for any proper smooth formal scheme over , where is the ring of integers in a complete discretely valued nonarchimedean extension of with perfect residue field and ramification degree , the -th Breuil–Kisin cohomology group and its Hodge–Tate specialization admit nice decompositions when . 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 satisfies , which generalizes the case of schemes under the condition proven by Fontaine and Messing (1987) and Caruso (2008).
Citation
Yu Min. "Integral -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
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