English

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.

Keywords

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

R2 v1 2026-06-22T05:42:44.304Z