On sheafification of modules

Prest, Mike and Ralph, Alexandra (2010) On sheafification of modules. [MIMS Preprint]

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We consider the localisation of the category of presheaves of modules over a ringed space to the category of sheaves of modules. With a suitable finiteness condition (being "elementary") on the torsion theory, we deduce that over noetherian spaces the latter category is locally finitely presented. This account is some of the background to our preprint "M. Prest and A. Ralph, Locally finitely presented categories of sheaves of modules" and to that of Philip Bridge, "Local presentability of categories of sheaves of modules".

Item Type: MIMS Preprint
Uncontrolled Keywords: ringed space, presheaf, sheaf, module, Grothendieck category, localisation, elementary torsion theory, finite type torsion theory, locally finitely presented, noetherian space
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 14 Algebraic geometry
MSC 2010, the AMS's Mathematics Subject Classification > 16 Associative rings and algebras
MSC 2010, the AMS's Mathematics Subject Classification > 18 Category theory; homological algebra
Depositing User: Professor Mike Prest
Date Deposited: 15 Feb 2010
Last Modified: 08 Nov 2017 18:18
URI: https://eprints.maths.manchester.ac.uk/id/eprint/1411

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