Rigid cohomology via the tilting equivalence

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.

Minor changes. Published. 25 pages

References in corpus (1)

• Integral p-adic Hodge theory

Cited by in corpus (2)

• Rigidity for rigid analytic motives
• The Berkovich realization for rigid analytic motives