Yuta Kimura, Osaka Metropolitan University

Title: Classifying torsion classes of Noetherian algebras

Abstract: 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 modA. 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.

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