Tuesday, June 28, 14:00

Michal Hrbek (Czech Academy of Sciences, Prague)
Topological endomorphism rings of large tilting complexes.

Abstract:
Following the recent result of Positselski and Šťovíček, we 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.