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arXiv · 2501.15569

Symmetric quasi-coherent sheaves

Grigory Garkusha
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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.

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Grigory Garkusha. 2025-01-26. Symmetric quasi-coherent sheaves. https://arxiv.org/abs/2501.15569

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