Let R be a commutative Noetherian ring and A a Noetherian R-algebra. In this talk, we study classification of torsion classes, torsion free classes and Serre subcategories of mod-A. In the case where A = R, such subcategories were classified by Gabriel, Takahashi and Stanley-Wang by using prime ideals of R. If R is a field, then A is a finite-dimensional algebra, and there are many studies of such subcategories relating with tilting theory. For a Noetherian algebra case, localization of A at a prime ideal of R plays an important role. We see that classification can be reduced to finite dimensional algebras. If A is commutative, our results cover cases of commutative rings.
This is joint work with Osamu Iyama.
This video was produced by the Okinawa Institute of Science and Technology, as part of their OIST Representation Theory Seminar series.
