A categorical Künneth formula for constructible Weil sheaves

Hemo, Tamir; Richarz, Timo; Scholbach, Jakob

doi:10.2140/ant.2024.18.499

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A categorical Künneth formula for constructible Weil sheaves

Tamir Hemo, Timo Richarz and Jakob Scholbach

Vol. 18 (2024), No. 3, 499–536

DOI: 10.2140/ant.2024.18.499

Abstract

We prove a Künneth-type equivalence of derived categories of lisse and constructible Weil sheaves on schemes in characteristic $p > 0$ for various coefficients, including finite discrete rings, algebraic field extensions $E \supset ℚ_{ℓ}$ , $ℓ \neq p$ , and their rings of integers $𝒪_{E}$ . We also consider a variant for ind-constructible sheaves which applies to the cohomology of moduli stacks of shtukas over global function fields.

Keywords

Weil sheaves, Künneth formula

Mathematical Subject Classification

Primary: 14D24, 14F20, 14F35

Milestones

Received: 20 February 2022

Revised: 23 March 2023

Accepted: 29 May 2023

Published: 16 February 2024

Authors

Tamir Hemo
Department of Mathematics California Institute of Technology Pasadena, CA United States

Timo Richarz
Department of Mathematics Technical University of Darmstadt Darmstadt Germany

Jakob Scholbach
Dipartimento di Matematica University of Padova Padova Italy

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Vol. 18, No. 3, 2024