English

A note on linear stacks

Algebraic Geometry 2021-10-25 v2 Algebraic Topology K-Theory and Homology

Abstract

In this brief note, we investigate graded functions of linear stacks in derived geometry. In particular, we show that under mild assumptions, we can recover a quasi-coherent sheaf on a derived stack from the data of the Gm\mathbb{G}_m-graded linear stack associated to it. Then we generalize this result in null caracteristic by describing graded functions on linear stacks.

Keywords

Cite

@article{arxiv.2103.06555,
  title  = {A note on linear stacks},
  author = {Ludovic Monier},
  journal= {arXiv preprint arXiv:2103.06555},
  year   = {2021}
}

Comments

Some details were added and the proof of Proposition 2.11 was corrected

R2 v1 2026-06-23T23:59:25.628Z