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2010.22: On sheafification of modules

2010.22: Mike Prest and Alexandra Ralph (2010) On sheafification of modules.

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Abstract

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 2000 > 14 Algebraic geometry
MSC 2000 > 16 Associative rings and algebras
MSC 2000 > 18 Category theory; homological algebra
MIMS number:2010.22
Deposited By:Professor Mike Prest
Deposited On:15 February 2010

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