Rigidity for rigid analytic motives

Abstract

In this paper we prove the Rigidity Theorem for motives of rigid analytic varieties over a non-Archimedean valued field $K$. We prove this theorem both for motives with transfers and without transfers in a relative setting. Applications include the construction of étale realization functors, an upgrade of the known comparison between motives with and without transfers and an upgrade of the rigid analytic motivic tilting equivalence, extending them to $\mathrm{Z}[1/p]$-coefficients.

Minor changes. Accepted for publication in J. Inst. Math. Jussieu. 24 pages

References in corpus (4)

• Rigid cohomology via the tilting equivalence
• Log smoothness and polystability over valuation rings
• Homotopy theory of dg sheaves
• The Berkovich realization for rigid analytic motives

Cited by in corpus (2)

• The six-functor formalism for rigid analytic motives
• The Berkovich realization for rigid analytic motives