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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
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 , p, and their rings of integers 𝒪E. 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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