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.