PreprintCC BY 4.0arXiv
Six-functor formalism for Kummer étale cohomology of log schemes
Abstract
We establish a Grothendieck six-functor formalism for Kummer étale cohomology including Poincaré duality for every separated vertical exact log smooth morphism of noetherian fs log schemes f: X→ S when the coefficient ring Λ is killed by an integer invertible on S. This is done via log étale rigidity Dlacuteet(S,Λ)≃ DAlacuteet(S,Λ). To achieve this, we also prove that Kummer étale cohomology satisfies 𝔸1-invariance, invariance under virtual isomorphisms, log cdh-descent, and invariance under verticalization.
Related
BibTeX
@misc{park2026sixfunctor,
title = {{Six-functor formalism for Kummer étale cohomology of log schemes}},
author = {Doosung Park},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29386},
eprint = {2608.29386},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29386},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Six-functor formalism for Kummer étale cohomology of log schemes
AU - Doosung Park
PY - 2026
DA - 2026/08/29
PB - arXiv
DO - 10.48550/arxiv.2608.29386
UR - https://arxiv.org/abs/2608.29386
AB - We establish a Grothendieck six-functor formalism for Kummer étale cohomology including Poincaré duality for every separated vertical exact log smooth morphism of noetherian fs log schemes f: X→ S when the coefficient ring Λ is killed by an integer invertible on S. This is done via log étale rigidity D_lacuteet(S,Λ)≃ DA_lacuteet(S,Λ). To achieve this, we also prove that Kummer étale cohomology satisfies 𝔸^1-invariance, invariance under virtual isomorphisms, log cdh-descent, and invariance under verticalization.
ER -