The stable category of Gorenstein flat sheaves on a noetherian scheme

2019/04/16 by Christensen, Lars Winther, Estrada, Sergio, Thompson, Peder
#14F05 #18G35 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1904.07661

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.

Related

• Totally acyclic complexes over noetherian schemes
• Homotopy categories of totally acyclic complexes with applications to\n the flat-cotorsion theory
• An Alternative Model for Coherent Sheaves over Noetherian Schemes
• The stable derived category of a noetherian scheme
• Quillen equivalences inducing Grothendieck duality for unbounded chain complexes of sheaves