Computing the cohomology of constructible étale sheaves on curves
Year: 2025
Type: article
Abstract: We present an explicit expression for 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 this complex and study its complexity. We illustrate this algorithm with several examples.
DOI: 10.5802/jtnb.1309
Author: Christophe Levrat
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4409004211