Computing the cohomology of constructible \'etale sheaves on curves
Algebraic Geometry
2026-02-16 v2 Number Theory
Abstract
We present an explicit expression of the cohomology complex of a constructible sheaf of abelian groups on the small \'etale 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.
Keywords
Cite
@article{arxiv.2306.03283,
title = {Computing the cohomology of constructible \'etale sheaves on curves},
author = {Christophe Levrat},
journal= {arXiv preprint arXiv:2306.03283},
year = {2026}
}