Silting theory was first introduced by Keller and Vossieck in the classification of certain t-structures. Silting objects can be equipped with a notion of mutation, which also relates them to cluster theory and tilting theory. For a finite-dimensional algebra Λ over an algebraically closed field k, a special role is played by the set of basic 2-term silting complexes–it is in bijection with the set of functorially finite torsion classes in mod Λ, which, if finite, is the set of all torsion classes in mod Λ. In this case, since the set of torsion classes is a lattice, the set of basic 2-term silting complexes forms a lattice as well. As
a part of my M2 thesis with Pierre-Guy Plamondon, I am trying to generalize these results to the set of d-term silting complexes for larger values of d. In particular, we replace the notion of torsion classes in mod Λ with Adachi, Enomoto, and Tsukamoto’s notion of ‘s-torsion pairs’ in certain ‘truncated’ derived categories of mod Λ. Our goal is to find a class that generalizes the class of functorially finite torsion classes and to show that this class is a lattice under nice conditions. Since my French vocabulary is a bit limited at the moment, the presentation will be in English. However, everyone is more than welcome to
ask questions/clarifications in French.