On pristine morphisms
Algebraic Geometry
2026-03-20 v2 Commutative Algebra
Abstract
We investigate flat morphisms of schemes of positive characteristic whose relative Frobenius is an isomorphism, which we call pristine. We show that these give rise to a natural Grothendieck topology that is fine tuned for the localization of Cartier modules.
Keywords
Cite
@article{arxiv.2512.06063,
title = {On pristine morphisms},
author = {Javier Carvajal-Rojas and Axel Stäbler},
journal= {arXiv preprint arXiv:2512.06063},
year = {2026}
}
Comments
22 pages, v2: changed title; we added a discussion showing that $F$-singularity invariants transform nicely under pristine morphisms