Categorical Künneth formulas for cohomological motives

Abstract

The manuscript at hand systematically studies Künneth formulas at a categorical level. We give criteria for an abstract six functor formalism to satisfy the categorical Künneth formula, and use this to formulate conjectures for categories of étale motives. As supporting evidence for these conjectures, we prove categorical Künneth formulas for adic sheaves and for cohomological motives, i.e., étale motives modulo the kernel of the adic realization.

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