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Article Dans Une Revue Journal of Pure and Applied Algebra Année : 2019

Rigid cohomology via the tilting equivalence

Résumé

We define a de Rham cohomology theory for analytic varieties over a valued field K ♭ of equal characteristic p with coefficients in a chosen untilt of the perfection of K ♭ by means of the motivic version of Scholze's tilting equivalence. We show that this definition generalizes the usual rigid cohomology in case the variety has good reduction. We also prove a conjecture of Ayoub yielding an equivalence between rigid analytic motives with good reduction and unipotent algebraic motives over the residue field, also in mixed characteristic.
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Dates et versions

hal-03895754 , version 1 (13-12-2022)

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Alberto Vezzani. Rigid cohomology via the tilting equivalence. Journal of Pure and Applied Algebra, 2019, 223 (2), pp.818-843. ⟨10.1016/j.jpaa.2018.05.001⟩. ⟨hal-03895754⟩
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