Rigidity for rigid analytic motives

TL;DR

This paper proves the Rigidity Theorem for motives of rigid analytic varieties over non-Archimedean fields, enabling new applications like étale realization functors and extending motivic tilting equivalences.

Contribution

It establishes the Rigidity Theorem for rigid analytic motives with and without transfers, extending existing results to include $ ext{Z}[1/p]$-coefficients.

Findings

Proved the Rigidity Theorem for rigid analytic motives.

Constructed étale realization functors for these motives.

Extended motivic tilting equivalence to $ ext{Z}[1/p]$-coefficients.

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 \'etale 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.