Title: Topological endomorphism rings of large tilting
Abstract: Following the recent result of Positselski and
study the (large) tilting complexes whose hearts are
contramodules in the sense of Positselski. It so happens that
examples of tilting complexes for which the heart cannot be a
of contramodules over any complete and separated topological
However, we introduce a condition which ensures that the
equivalent to the category of right contramodules over the
ring of the tilting complex endowed with a suitable topology.
setting of the derived category of a ring, our condition
turns out to
have a rather natural characterization: it is satisfied by
complexes whose character dual is cotilting. Furthermore, the
heart is then equivalent to another category induced by the
topology - the category of discrete modules. If time permits,
some examples coming from commutative algebra.