Computing the cohomology of constructible étale sheaves on curves

Fuente: arXiv
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Main Author: Levrat, Christophe
Format: Preprint
Published: 2023
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_version_ 1866914327993253888
author Levrat, Christophe
author_facet Levrat, Christophe
contents We present an explicit expression of the cohomology complex of a constructible sheaf of abelian groups on the small étale site of an irreducible curve over an algebraically closed field, when the torsion of the sheaf is invertible in the field. This expression only involves finite groups, and is functorial in both the curve and the sheaf. In particular, we explain how to compute the Galois action on this complex. We also present an algorithm which computes it and study its complexity.
format Preprint
id arxiv_https___arxiv_org_abs_2306_03283
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Computing the cohomology of constructible étale sheaves on curves
Levrat, Christophe
Algebraic Geometry
Number Theory
14F20, 11G20, 11Y16, 03D99
We present an explicit expression of the cohomology complex of a constructible sheaf of abelian groups on the small étale site of an irreducible curve over an algebraically closed field, when the torsion of the sheaf is invertible in the field. This expression only involves finite groups, and is functorial in both the curve and the sheaf. In particular, we explain how to compute the Galois action on this complex. We also present an algorithm which computes it and study its complexity.
title Computing the cohomology of constructible étale sheaves on curves
topic Algebraic Geometry
Number Theory
14F20, 11G20, 11Y16, 03D99
url https://arxiv.org/abs/2306.03283