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Seminario MALGA Padova Verona - Moduli Algebre Anelli

Martedi' 28 Settembre 2010 - J. Trlifaj, A. Tonolo

ARGOMENTI: Seminari

Martedi' 28 settembre 2010 - Aula 2AB40 Torre Archimede

ore 15:00
Jan Trlifaj (Charles University, Prague)
"Tilting for commutative noetherian rings"

-Abstract
Tilting over commutative rings has for a long time been considered trivial, for in this case, there are no non-projective finitely generated tilting modules. But the picture changes completely once we broaden our horizons to infinitely generated modules. Not only that approximation theory and category equivalences are still available in this generality, but a complete classification is possible in many cases. In this talk, we will start by the relevant general results, and then deal in detail with the case of commutative noetherian rings.

ore 16:30
Alberto Tonolo (Universita' di Padova)
"When is the heart of a faithful torsion pair a module category?"

-Abstract
In 1982 Beilinson, Bernstein and Deligne have proved that the heart H(X,Y) of a faithful torsion pair (X,Y) is an abelian category. In 2009 Colpi and Gregorio have proved that H(X,Y) is a Grothendieck category if and only if the torsion free class Y is cogenerated by a 1-cotilting module. Recently in a joint paper with Colpi and Mantese we have found necessary and sufficient conditions for H(X,Y) to be equivalent to a module category. In this talk I will describe the results obtained.

Rif. int. S. Bazzoni

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