The stable category of Gorenstein flat sheaves on a noetherian scheme
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2019
- DOI:
- 10.48550/arXiv.1904.07661
- arXiv:
- arXiv:1904.07661
- Bibcode:
- 2019arXiv190407661W
- Keywords:
-
- Mathematics - Commutative Algebra;
- Mathematics - Algebraic Geometry;
- 14F05;
- 18G35
- E-Print:
- Final version, to appear in Proc. Amer. Math. Soc.