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The projective stable category of a coherent scheme

Part of: Homological algebra

Published online by Cambridge University Press:  26 February 2018

Sergio Estrada  and
James Gillespie
Sergio Estrada
Affiliation:
Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, Murcia 30100, Spain (sestrada@um.es)
James Gillespie
Affiliation:
School of Theoretical and Applied Science, Ramapo College of New Jersey, 505 Ramapo Valley Road, Mahwah, NJ 07430, USA (jgillesp@ramapo.edu)
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Abstract

We define the projective stable category of a coherent scheme. It is the homotopy category of an abelian model structure on the category of unbounded chain complexes of quasi-coherent sheaves. We study the cofibrant objects of this model structure, which are certain complexes of flat quasi-coherent sheaves satisfying a special acyclicity condition.

Keywords

coherent schemeGorenstein flatquasi-coherent sheafabelian model structure

MSC classification

Primary: 18G35: Chain complexes
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 149 , Issue 1 , February 2019 , pp. 15 - 43
Copyright
Copyright © Royal Society of Edinburgh 2018 

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