Tuesday, June 28, 14:00
Michal Hrbek (Czech Academy of Sciences, Prague)
Topological endomorphism rings of large tilting complexes.
Following the recent result of Positselski and
study the (large) tilting complexes whose hearts are categories of
contramodules in the sense of Positselski. It so happens that there are
examples of tilting complexes for which the heart cannot be a category
of contramodules over any complete and separated topological ring.
However, we introduce a condition which ensures that the heart is
equivalent to the category of right contramodules over the endomorphism
ring of the tilting complex endowed with a suitable topology. In the
setting of the derived category of a ring, our condition turns out to
have a rather natural characterization: it is satisfied by those silting
complexes whose character dual is cotilting. Furthermore, the cotilting
heart is then equivalent to another category induced by the same linear
topology - the category of discrete modules. Finally, we show that the
decent tilting complexes parametrize certain class of derived equivalences
to contramodule categories.