The six-functor formalism for rigid analytic motives

Abstract

We offer a systematic study of rigid analytic motives over general rigid analytic spaces, and we develop their six-functor formalism. A key ingredient is an extended proper base change theorem that we are able to justify by reducing to the case of algebraic motives. In fact, more generally, we develop a powerful technique for reducing questions about rigid analytic motives to questions about algebraic motives, which is likely to be useful in other contexts as well. We pay special attention to establishing our results without noetherianity assumptions on rigid analytic spaces. This is indeed possible using Raynaud's approach to rigid analytic geometry.

188 pages. This version incorporates an erratum to the journal version of the article (the hypotheses of Lemma 2.1.4 have been modified; all the other results are unaffected)

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Cited by in corpus (8)

• The six-functor formalism for rigid analytic motives
• Motivic Homotopy Theory of Algebraic Stacks
• On the Nori and Hodge realisations of Voevodsky motives
• Remarks on étale motivic stable homotopy theory
• A motivic proof of the finiteness of relative de Rham cohomology
• The de Rham-Fargues-Fontaine cohomology
• An introduction to six-functor formalisms
• An axiomatization of six-functor formalisms