Computing the cohomology of constructible \'etale sheaves on curves - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

Computing the cohomology of constructible \'etale sheaves on curves

Résumé

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.

Dates et versions

hal-04286657 , version 1 (15-11-2023)

Identifiants

Citer

Christophe Levrat. Computing the cohomology of constructible \'etale sheaves on curves. 2023. ⟨hal-04286657⟩
20 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More