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.
Rigid cohomology via the tilting equivalence / A. Vezzani. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - 223:2(2019 Feb), pp. 818-843. [10.1016/j.jpaa.2018.05.001]
Rigid cohomology via the tilting equivalence
A. Vezzani
2019
Abstract
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.File | Dimensione | Formato | |
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