Tuesday, January 31, 14:00, 7.527
Jan Stovicek (Prague),
A tilting-cotilting correspondence and tilting in infinite projective
This is an account on joint work with Leonid Positselski. We show that
there is a very general version of Rickard's tilting theorem which involves
cotilting objects in Grothendieck-like abelian categories on one hand and
tilting objects in categories of contramodules on the other hand.
Contramodules are roughly speaking modules over rings with infinitary
addition - complete topological modules over complete topological rings are
contramodules, but the notion is broader than that.
If the tilting and cotilting modules have finite homological dimensions,
one obtains usual derived equivalences. In case of infinite homological
dimensions, these concepts generalize Wakamatsu tilting modules and there
is still a triangulated equivalence. This equivalence, however, is not
necessarily between ordinary derived categories, but between Positselski's
"exotic" derived categories.