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 ⊃ ℚℓ, ℓ ≠ 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.
A categorical Künneth formula for constructible Weil sheaves
Jakob Scholbach
2024
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 ⊃ ℚℓ, ℓ ≠ 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.
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