Purity in categories of sheaves
Algebraic Geometry
2019-06-06 v2 Category Theory
Logic
Representation Theory
Abstract
We consider categorical and geometric purity for sheaves of modules over a scheme satisfying some mild conditions, both for the category of all sheaves and for the category of quasicoherent sheaves. We investigate the relations between these four purities and compute a number of examples, in particular describing both the geometric and categorical Ziegler spectra for the category of quasicoherent sheaves over the projective line over a field.
Keywords
Cite
@article{arxiv.1809.08981,
title = {Purity in categories of sheaves},
author = {Alexander Slavik and Mike Prest},
journal= {arXiv preprint arXiv:1809.08981},
year = {2019}
}