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- W3159729043 abstract "The purpose of this paper is to prove a basic $p$-adic comparison theorem for smooth rigid analytic and dagger varieties over the algebraic closure $C$ of a $p$-adic field: $p$-adic pro-etale cohomology, in a stable range, can be expressed as a filtered Frobenius eigenspace of de Rham cohomology (over $bf{B}^+_{rm dR}$). The key computation is the passage from absolute crystalline cohomology to Hyodo-Kato cohomology and the construction of the related Hyodo-Kato isomorphism. We also geometrize our comparison theorem by turning $p$-adic pro-etale and syntomic cohomologies into sheaves on the category ${rm Perf}_C$ of perfectoid spaces over $C$ (this geometrization will be crucial in our proof of the $C_{rm st}$-conjecture in the sequel to this paper)." @default.
- W3159729043 created "2021-05-10" @default.
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- W3159729043 date "2021-11-16" @default.
- W3159729043 modified "2023-09-27" @default.
- W3159729043 title "On the cohomology of $p$-adic analytic spaces, I: The basic comparison theorem" @default.
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