E. Gupta - On higher 𝜏-tilting finite algebras

Building up on the definition of support 𝜏-tilting pairs by Adachi, Iyama, and Reiten, 𝜏-tilting finite algebras were defined by Demonet, Iyama, and Jasso as algebras which contain finitely many such pairs, or equivalently, finitely many 2-term silting objects. They proved several properties and characterisations of such algebras, including the fact that an algebra is 𝜏-tilting finite if and only if all the torsion classes in the module category are functorially finite. Recently, the bijections of Adachi, Iyama, and Reiten were generalised to extended module categories along with appropriate definitions of 𝜏-tilting pairs and torsion classes in this higher setting. In this talk, our goal will be to generalise the results of Demonet, Iyama, and Jasso to “𝜏𝑑 -tilting finite algebras", i.e., algebras with finitely many 𝑑-term silting objects. https://if-summer-2026.sciencesconf.org/