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Potential semi-stability ofp-adic étale cohomology

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Abstract

We extend the methods of Faltings and Tsuji, and prove that ifK is a field of characteristic 0 with a complete, discrete valuation, and a perfect residue field of characteristicp, then thep-adic étale cohomology of a finite typeK-scheme is potentially semi-stable. We prove a similar result for cohomology with compact support, and for cohomology with support in a closed subspace ofX. We establish a relationship between these cohomology groups, and the de Rham cohomology ofX.

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  1. SFB 478, Westfälische Wilhelms-Universität, Hittorfstrasse 27, D-48149, Münster, Germany

    Mark Kisin

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  1. Mark Kisin
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Correspondence to Mark Kisin.

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Kisin, M. Potential semi-stability ofp-adic étale cohomology. Isr. J. Math. 129, 157–173 (2002). https://doi.org/10.1007/BF02773161

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