Descent for algebraic stacks
Algebraic Geometry
2026-01-09 v2 Number Theory
Abstract
We prove that algebraic stacks satisfy 2-descent for fppf coverings. We generalize Galois descent for schemes to stacks, by considering the case where the fppf covering is a finite Galois covering, and reformulating 2-descent data in terms of Galois group actions on the stack.
Keywords
Cite
@article{arxiv.2504.13642,
title = {Descent for algebraic stacks},
author = {Olivier de Gaay Fortman},
journal= {arXiv preprint arXiv:2504.13642},
year = {2026}
}
Comments
16 pages, final version, to appear in Comptes Rendus Math\'ematique