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International Conference on Algebra and its Applications
March 25-28, 1999
Ohio University
Athens, OH, USA |
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Organizers
Dinh Van Huynh, S.K. Jain, Sergio Lopez-Permouth
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Tilting equivalences for Grothendieck categories
by
Enrico Gregorio
University of Verona (Italy)
Let C1 and C2 be Grothendieck categories and let
(Ti, Fi) be a torsion theory on Ci (i=1, 2).
Assume that:
- there exists an equivalence between T1 and F2:
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F:T1 --> F2, G:F2 --> T1; |
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- the closure of T1 under subobjects is C1;
- the closure of F2 under quotients is C2.
Then it is possible to extend F and G to the whole categories and to obtain an
abstract version of the ``Tilting Theorem''. In particular it is possible to define
the left derived functor of G, even if C2 has not enough projectives
and the derived functors of F and G induce an equivalence between
F1 and T2.
The abstract case is applied to closed categories of modules, obtaining the notion
of topological tilting module.
Date received: February 7, 1999
Copyright © 1999 by the author(s).
The author(s) of this document and the organizers of the conference
have granted their consent to include this abstract in
Atlas Conferences Inc.
Document # cabw-69.