2010.22: On sheafification of modules
2010.22: Mike Prest and Alexandra Ralph (2010) On sheafification of modules.
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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 2000 > 14 Algebraic geometry|
MSC 2000 > 16 Associative rings and algebras
MSC 2000 > 18 Category theory; homological algebra
|Deposited By:||Professor Mike Prest|
|Deposited On:||15 February 2010|