Rosanna Laking - University of Verona
Limits of cosilting complexes and colimits of silting
complexes
Abstract: I will present joint work with Alexandra Zvonareva in
which we show how to construct new (co)silting complexes from a
sequence of (co)silting complexes whose (co)silting classes form a
chain. This work is motivated by finite-dimensional algebras whose
g-vector fan is dense in R^n. Taking a point P of R^n that is
outside the g-vector fan, we can construct such sequences of
(co)silting classes determined by a converging sequence of points
inside the g-vector fan; I will explain how the newly constructed
(co)silting complex can be seen to represent the point P
Sergio Pavon, -University of Verona
Detecting derived equivalences via the CHZ criterion
Abstract:
Let $A$ be an abelian category, and $(T,F)$ a torsion pair in
$A$. Following
Happel, Reiten and Smalø, one can use $(T,F)$ to deform $A$ into
a new abelian
category $B=F*T[-1]$. In most concrete situations, there is a
functor $D^b(B)\to
D^b(A)$ between the derived categories of $A$ and $B$, and one
can ask if it is
an equivalence, for example because this means that $A$ and $B$,
despite being
possibly very different, share the same derived invariants.
In 2019, Chen, Han and Zhou obtained a criterion to detect when
a torsion pair
induces an equivalence between derived categories. This
criterion is internal to
the category $A$ (that is, it does not appeal to $D^b(A)$). In
this talk we aim
to showcase a few applications of this criterion in various
settings (often,
over finite-dimensional algebras), to convince the audience that
it is a practical
tool with useful applications.