Cluster Colloquium

Thursday 08.Jan.2026, 17:00 Central European Time

The lattice of torsion pairs and the Ziegler spectrum

Lidia Angeleri Hügel (Università degli Studi di Verona).

Abstract. Over a finite dimensional algebra A, the torsion pairs in the category mod(A) of finite

dimensional modules form a complete lattice tors(A). It is an important invariant of A which

encodes relevant information on the category of A-modules and its derived category D(A).

In my talk, I will discuss the connection of tors(A) with another important invariant, the

Ziegler spectrum Zg(D(A)) of D(A). This is a topological space originating from the model theory

of modules that describes the theory of purity of D(A).

We will see that certain distinguished intervals in tors(A) correspond to closed sets in Zg(D(A)),

and we will describe the arrows in the Hasse quiver of tors(A) in terms of an operation of mutation.

If time permits, I will also present an application to the theory of stability.

This is a report on joint work with Rosanna Laking, Calvin Pfeifer, and Francesco Sentieri.