2023/06/05 by Christophe Levrat, Levrat, Christophe · 3 citations
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Topological and Geometric Data Analysis #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2306.03283
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.