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Seminario MALGA Padova Verona - Moduli Algebre Anelli: The ordered K-series for a ring + Model approximations for relative homological algebra

Giovedì 19 Marzo 2015, ore 15:00 - Aula 1BC45 - Peter Vamos + Simone Virili

ARGOMENTI: Seminari

Giovedì 19 marzo 2015 in Aula 1BC45 si terrà un incontro del Seminario Padova - Verona MALGA Moduli Algebre Anelli

ore 15:00
Peter Vamos (Exeter University)
"The ordered K-series for a ring"
Abstract
The ordered K-group of a (module) category is the universal partially ordered group for the additive and non-negative invariants on that category. Additionally it not only encapsulates these invariants but induces both a descending and an ascending chain of subcategories indexed by ordinal numbers. This way it also yields a dimension which is an ordinal number. This generalises the Gabriel-Rentschler Krull dimension when the staring category is the Serre category generated by the finitely generated modules; for example, unlike the Gabriel-Rentschler Krull dimension, it can assign the (correct) dimension to non-discrete valuation rings. When the category is that of modules with finite free resolution then this dimension behaves like grade.

ore 16:30
Simone Virili (Università di Padova)
"Model approximations for relative homological algebra"
Abstract
Recently, Chacholski, Neeman, Pitsch, and Scherer studied, in a series of three papers, model approximations (a generalization of the concept of model structure on a given category with a fixed choice of weak equivalences) for the unbounded category of cochain complexes over a commutative ring. These approximations allow to construct relative injective resolutions with respect to particular choices of "relatively injective modules". In this seminar we define similar model approximations for cochain complexes on general Grothendieck categories generalizing the previous constructions and reaching a better understanding of the whole picture. This seminar is based on a preprint (with the same title of the seminar) available at: http://arxiv.org/pdf/1401.7432v1.pdf