# The stable category of Gorenstein flat sheaves on a noetherian scheme

## TL;DR

This paper establishes that the category of cotorsion Gorenstein flat quasi-coherent sheaves on a semi-separated noetherian scheme is Frobenius, extending the theory of Gorenstein homological algebra to a non-affine geometric setting.

## Contribution

It introduces a Frobenius category structure for cotorsion Gorenstein flat sheaves on schemes, generalizing known module theory results to algebraic geometry.

## Key findings

- The category of cotorsion Gorenstein flat sheaves is Frobenius.
- This category aligns with the pure derived category of F-totally acyclic complexes.
- It provides a non-affine analogue of Gorenstein projective modules.

## 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.