Approximation of sheaves on algebraic stacks
Algebraic Geometry
2016-09-01 v3
Abstract
Raynaud--Gruson characterized flat and pure morphisms between affine schemes in terms of projective modules. We give a similar characterization for non-affine morphisms. As an application, we show that every quasi-coherent sheaf is the union of its finitely generated quasi-coherent subsheaves on any quasi-compact and quasi-separated algebraic stack.
Cite
@article{arxiv.1408.6698,
title = {Approximation of sheaves on algebraic stacks},
author = {David Rydh},
journal= {arXiv preprint arXiv:1408.6698},
year = {2016}
}
Comments
17 pages; generalized result to all quasi-compact and quasi-separated algebraic stacks; added some applications; major revision; final version