Algebra/Topology Seminar

Sergio Estrada (Universidad de Murcia)

Title: "The stable category of Gorenstein flat sheaves on a noetherian scheme"

Abstract: A classical result due to Buchweitz says that the singularity category of a Gorenstein local ring A is equivalent to the homotopy category of totally acyclic complexes of finitely generated projective modules. The latter is also equivalent to the stable category of finitely generated Gorenstein projective modules. This second equivalence extends for general noetherian rings and without the finiteness assumption on the modules. In 2011 Murfet and Salarian introduced an optimal non-affine replacement for the homotopy category of totally acyclic complexes of projectives. But the question of the non-affine analogue for the stable category of Gorenstein projective modules remained open. In the talk we will propose and show evidences to justify that the stable category of cotorsion and Gorenstein flat quasi-coherent sheaves is one natural candidate for this. As an application, we give a characterization of Gorenstein schemes by using these sheaves.

This talk is based on a joint work with Lars Winther Christensen and Peder Thompson