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Ind-abelian categories and quasi-coherent sheaves

Published online by Cambridge University Press:  02 October 2014

DANIEL SCHÄPPI
DANIEL SCHÄPPI*
Affiliation:
e-mail: dschaepp@uwo.ca
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Abstract

We study the question of when a category of ind-objects is abelian. Our answer allows a further generalization of the notion of weakly Tannakian categories introduced by the author. As an application we show that, under suitable conditions, the category of coherent sheaves on the product of two schemes with the resolution property is given by the Deligne tensor product of the categories of coherent sheaves of the two factors. To do this we prove that the class of quasi-compact and semi-separated schemes with the resolution property is closed under fiber products.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 157 , Issue 3 , November 2014 , pp. 391 - 423
Copyright
Copyright © Cambridge Philosophical Society 2014 

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