Torsion pairs are fundamental tools in the study of abelian categories, which contain important information related to derived categories and their t-structures. In this talk we will consider the lattice of torsion classes in the category of finite-dimensional modules over a finite-dimensional algebra, with a particular focus on the minimal inclusions of torsion classes.
It was shown by Adachi, Iyama and Reiten that minimal inclusions of functorially finite torsion classes correspond to irreducible mutations of associated two-term silting complexes in the category of perfect complexes. In this talk we will explain how minimal inclusions of arbitrary torsion classes correspond to irreducible mutations of associated two-term cosilting complexes in the unbounded derived category.
This talk will be based on joint work with Lidia Angeleri Hügel, Jan Stovicek and Jorge Vitória.
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