Symmetric quasi-coherent sheaves
Abstract
Using methods of stable homotopy theory, the category of symmetric quasi-coherent sheaves associated with non-commutative graded algebras with extra symmetries is introduced and studied in this paper. It is shown to be a closed symmetric monoidal Grothendieck category with invertible generators. It is proven that the category of quasi-coherent sheaves on a projective scheme is recovered out of symmetric quasi-coherent sheaves. As an application, symmetric projective schemes associated to such algebras are introduced and studied. It is shown that classical projective schemes are recovered from symmetric ones.
Cite
@article{arxiv.2501.15569,
title = {Symmetric quasi-coherent sheaves},
author = {Grigory Garkusha},
journal= {arXiv preprint arXiv:2501.15569},
year = {2025}
}
Comments
Section 7 has been added, in which symmetric projective schemes associated to non-commutative graded algebras with extra symmetries are introduced. They recover the classical ones