The stable category of Gorenstein flat sheaves on a noetherian scheme
Commutative Algebra
2020-07-16 v2 Algebraic Geometry
Abstract
For a semi-separated 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 acyclic complexes of flat quasi-coherent sheaves as the natural non-affine analogue of the homotopy category of totally acyclic complexes of projective modules.
Keywords
Cite
@article{arxiv.1904.07661,
title = {The stable category of Gorenstein flat sheaves on a noetherian scheme},
author = {Lars Winther Christensen and Sergio Estrada and Peder Thompson},
journal= {arXiv preprint arXiv:1904.07661},
year = {2020}
}
Comments
Final version, to appear in Proc. Amer. Math. Soc.; 14 pp