Seminario MALGA Padova Verona - Moduli Algebre Anelli: “The tilting-cotilting correspondence and contramodule categories as the tilting hearts”

Mercoledì 31 Gennaio 2018, ore 15:00 - Aula 1BC50 - Leonid Positselski


Mercoledì 31 Gennaio 2018 alle ore 15:00 in Aula 1BC50, Leonid Positselski (University of Haifa and Institute for Information Transmission Problems, Moscow) terrà un seminario dal titolo “The tilting-cotilting correspondence and contramodule categories as the tilting hearts”, nell'ambito del Seminario Padova-Verona MALGA - Moduli Algebre Anelli.

The tilting-cotilting correspondence connects complete, cocomplete abelian categories A with an injective cogenerator and an n-tilting object, on the one hand, and complete, cocomplete abelian categories B with a projective generator and an n-cotilting object, on the other hand. Moreover, a similar bijective correspondence holds for n = infinity. When A is the category of modules over an associative ring (or, more generally, a locally finitely presentable Grothendieck abelian category), the corresponding abelian category B is the category of contramodules over the topological ring of endomorphisms of the tilting object.
The talk is expected to consist of two parts, with the first part devoted to an introductory discussion of contramodules, including the definition of a contramodule over a topological ring and other necessary preliminaries. The results about the tilting-cotilting correspondence and the role of contramodule categories in it will be presented in the second part.