Title: 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. If time permits,
we discuss
some examples coming from commutative algebra.