Classifying torsion classes of Noetherian algebras

Let R be a commutative Noetherian ring. A Noetherian algebra A is an R-algebra which is finitely generated as an R-module. In this talk, we study classification problem of torsion classes and related subcategories of the category mod A of finitely generated A-modules. In the case where R is a field, there are many studies of subcategories of mod A. τ-tilting modules, introduced by Adachi-Iyama-Reiten, play a central role in the recent development of such studies. We see that silting modules also play an important role for classification problem of torsion classes of Noetherian algebras. In the case where A is commutative, Serre subcategories, torsion classes and torsionfree classes are classified by using subsets of the prime spectrum of R by Gabriel, Stanley-Wang and Takahashi. We see that our results recover their results. This is joint work with Osamu Iyama.