# Torsion pairs and mutation

Every torsion pair in the category $$\operatorname{mod}A$$ of finitely generated modules over a noetherian ring $$A$$ corresponds bijectively to a torsion pair in the large module category $$\operatorname{Mod}A$$ which is determined by a large (that is, not necessarily compact) two-term cosilting complex in the unbounded derived category $$D(\operatorname{Mod}A)$$. Motivated by this observation, we investigate a notion of mutation for large cosilting objects in triangulated categories. In this context, mutation is not always possible: it is controlled by properties of certain torsion pairs in the heart of the t-structure induced by the cosilting object. In the case of two-term cosilting complexes in the derived category of a finite dimensional algebra $$A$$, these constraints lead to a new interpretation of wide intervals inside the lattice of torsion pairs in $$\operatorname{mod}A$$. The talk will be based on ongoing joint work with Rosanna Laking, Jan Šťovíček and Jorge Vitória.