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arXiv · 1904.07661

The stable category of Gorenstein flat sheaves on a noetherian scheme

Lars Winther Christensen·Sergio Estrada·Peder Thompson
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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.

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Lars Winther Christensen, Sergio Estrada, Peder Thompson. 2019-04-16. The stable category of Gorenstein flat sheaves on a noetherian scheme. https://arxiv.org/abs/1904.07661

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