The stable category of Gorenstein flat sheaves on a noetherian scheme
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- by Lars Winther Christensen, Sergio Estrada and Peder Thompson PDF
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Abstract:
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 acy- clic complexes of flat quasi-coherent sheaves as the natural non-affine analogue of the homotopy category of totally acyclic complexes of projective modules.References
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Additional Information
- Lars Winther Christensen
- Affiliation: Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409
- MR Author ID: 671759
- ORCID: 0000-0002-9360-123X
- Email: lars.w.christensen@ttu.edu
- Sergio Estrada
- Affiliation: Departamento de Matemáticas, Universidad de Murcia, Murcia 30100, Spain
- MR Author ID: 711614
- Email: sestrada@um.es
- Peder Thompson
- Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway
- MR Author ID: 1182639
- ORCID: 0000-0003-2714-9342
- Email: peder.thompson@ntnu.no
- Received by editor(s): April 16, 2019
- Received by editor(s) in revised form: April 17, 2019, June 16, 2019, and May 22, 2020
- Published electronically: December 14, 2020
- Additional Notes: The first author was partly supported by Simons Foundation collaboration grant 428308.
The second author was partly supported by grants PRX18/00057, MTM2016-77445-P, and 19880/GERM/15 by the Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia and FEDER funds - Communicated by: Jerzy Weyman
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 149 (2021), 525-538
- MSC (2020): Primary 14F08; Secondary 18G35
- DOI: https://doi.org/10.1090/proc/15258
- MathSciNet review: 4198062