The stable category of Gorenstein flat sheaves on a noetherian scheme

Abstract

For a semiseparated noetherian scheme, we show that the category of cotorsion Gorenstein flat quasi-coherent sheaves is Frobenius and a natural non-affine analogue of the category of Gorenstein projective modules over a noetherian ring. We show that this coheres perfectly with the work of Murfet and Salarian that identifies the pure derived category of F-totally acy- clic complexes of flat quasi-coherent sheaves as the natural non-affine analogue of the homotopy category of totally acyclic complexes of projective modules.

Description

© Copyright 2020 American Mathematical Society. This accepted manuscript is shared under a CC-BY-NC-ND license https://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords

Cotorsion Sheaf, Gorenstein Flat Sheaf, Noetherian Scheme, Stable Category, Totally Acyclic Complex

Citation

Christensen, L. W., Estrada, S., & Thompson, P. (2020). The stable category of Gorenstein flat sheaves on a noetherian scheme. Proceedings of the American Mathematical Society, 149(2), 525–538. https://doi.org/10.1090/proc/15258

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