The stable category of gorenstein flat sheaves on a noetherian scheme

Lars Winther Christensen, Sergio Estrada, Peder Thompson

Research output: Contribution to journalArticlepeer-review

Abstract

Abstrakt. For a semiseparated 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.

Original languageEnglish
Pages (from-to)525-538
Number of pages14
JournalProceedings of the American Mathematical Society
Volume149
Issue number2
DOIs
StatePublished - Feb 2021

Keywords

  • Cotorsion sheaf
  • Gorenstein flat sheaf
  • Noetherian scheme
  • Stable category
  • Totally acyclic complex

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