In this paper we prove the Rigidity Theorem for motives of rigid analytic varieties over a non-Archimedean valued field. 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-coefficients.
Rigidity for rigid analytic motives / F. Bambozzi, A. Vezzani. - In: JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU. - ISSN 1474-7480. - 20:4(2021 Jul), pp. 1341-1369. [10.1017/S1474748019000501]
Rigidity for rigid analytic motives
A. Vezzani
2021
Abstract
In this paper we prove the Rigidity Theorem for motives of rigid analytic varieties over a non-Archimedean valued field. 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-coefficients.
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