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arXiv · 2608.29386

Six-functor formalism for Kummer \'etale cohomology of log schemes

Doosung Park
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Abstract

We establish a Grothendieck six-functor formalism for Kummer \'etale cohomology including Poincar\'e duality for every separated vertical exact log smooth morphism of noetherian fs log schemes $f\colon X\rightarrow S$ when the coefficient ring $\Lambda$ is killed by an integer invertible on $S$. This is done via log \'etale rigidity \[\mathrm{D}_{\mathrm{l\acute{e}t}}(S,\Lambda)\simeq \mathrm{DA}_{\mathrm{l\acute{e}t}}(S,\Lambda).\] To achieve this, we also prove that Kummer \'etale cohomology satisfies $\mathbb{A}^1$-invariance, invariance under virtual isomorphisms, log cdh-descent, and invariance under verticalization.

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Doosung Park. 2026-08-29. Six-functor formalism for Kummer \'etale cohomology of log schemes. https://arxiv.org/abs/2608.29386

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