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Published online by Cambridge University Press:  27 September 2019

Federico Bambozzi
Mathematical Institute - University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, OxfordOX2 6GG, UK (
Alberto Vezzani
LAGA - Université Paris 13, Sorbonne Paris Cité, 99 av. Jean-Baptiste Clément, 93430Villetaneuse, France (


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 $\mathbb{Z}[1/p]$-coefficients.

Research Article
© The Author(s), 2019. Published by Cambridge University Press

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The first author acknowledges the University of Regensburg with the support of the DFG funded CRC 1085 ‘Higher Invariants. Interactions between Arithmetic Geometry and Global Analysis’. The second author was partially supported by the ANR Grant PERCOLATOR: ANR-14-CE25-0002-01 and by the ANR JCJC Grant PERGAMO: ANR-18-CE40-0017.


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