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Pure exact structures and the pure derived category of a scheme

Published online by Cambridge University Press:  23 November 2016

SERGIO ESTRADA ,
JAMES GILLESPIE  and
SINEM ODABAŞI
SERGIO ESTRADA
Affiliation:
Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, Espinardo, Murcia 30100, Spain. e-mail: sestrada@um.es
JAMES GILLESPIE
Affiliation:
Ramapo College of New Jersey, School of Theoretical and Applied Science, 505 Ramapo Valley Road, Mahwah, NJ 07430, U.S.A. e-mail: jgillesp@ramapo.edu
SINEM ODABAŞI
Affiliation:
Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Valdivia, Chile. e-mail: sinem.odabasi@uach.cl
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Abstract

Let $\mathcal{C}$ be closed symmetric monoidal Grothendieck category. We define the pure derived category with respect to the monoidal structure via a relative injective model category structure on the category C($\mathcal{C}$) of unbounded chain complexes in $\mathcal{C}$. We use λ-Purity techniques to get this. As application we define the stalkwise pure derived category of the category of quasi–coherent sheaves on a quasi-separated scheme. We also give a different approach by using the category of flat quasi–coherent sheaves.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 163 , Issue 2 , September 2017 , pp. 251 - 264
Copyright
Copyright © Cambridge Philosophical Society 2016 

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