The wall-chamber structures of the real Grothendieck groups

  • Sota Asai

    The University of Tokyo, Japan
The wall-chamber structures of the real Grothendieck groups cover
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Abstract

Let be a finite-dimensional algebra over a field . By using stability conditions for modules introduced by King, we can define the wall-chamber structure on the real Grothendieck group , as in the works of Brüstle, Smith and Treffinger, and of Bridgeland. In this article, we explain our result that the chambers in this wall-chamber structure are precisely the open cones associated to the basic 2-term silting objects in the perfect derived category . As one of the key steps, we introduce an equivalence relation, called TF equivalence, by using the numerical torsion pairs of Baumann–Kamnitzer–Tingley.