Sergio Pavon, University of Padova

Torsion-simple objects

Torsion pairs in abelian categories provide decompositions of objects, in a
torsion subobject and a torsion-free quotient. Given a family F of torsion
pairs, certain objects happen to be always either torsion or torsion-free with
respect to each pair in F; we call them the torsion-simple objects with respect
to F. Particular instances of this notion have appeared in the literature: to
give one example, the semistable objects of a stability function Z are the
torsion-simples with respect to a chain of torsion pairs associated to Z.
We will overview some torsion-simple objects in various settings
(over finite-dimensional algebras, over commutative noetherian rings, in some
Grothendieck hearts) with respect to various classes of torsion pairs (all, all
the hereditary ones, all the finite type ones, chains).

This talk is based on arxiv:2312.04384 .