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arXiv:2412.03382math.AG

Berkovich Motives

Peter Scholze

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Abstract

We construct a theory of (etale) Berkovich motives. This is closely related to Ayoub's theory of rigid-analytic motives, but works uniformly in the archimedean and nonarchimedean setting. We aim for a self-contained treatment, not relying on previous work on algebraic or analytic motives. Applying the theory to discrete fields, one still recovers the etale version of Voevodsky's theory. Two notable features of our setting which do not hold in other settings are that over any base, the cancellation theorem holds true, and under only minor assumptions on the base, the stable $\infty$-category of motivic sheaves is rigid dualizable.

arXiv comments
65 pages. final version, to appear in Journal of the AMS
Journal reference
DOI
Subjects
math.AGAlgebraic Geometry math.KTK-Theory and Homology math.NTNumber Theory

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  1. Mathematics is hard for mathematicians to understand too 1 comment

    • > I understand that some degree of formalism is required to enable the sharing of knowledge amongst people across a variety of languages, but sometimes I'll read a white paper and think "wow, this could be written a LOT more simply". OK, challenge accepted: find a way to write…

      aleph_minus_oneView on HNParent context

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