Tilting and Silting Theory of Noetherian Algebras

Kimura Y. Tilting and Silting Theory of Noetherian Algebras. International Mathematics Research Notices. 2023.We develop silting theory of a Noetherian algebra A over a commutative Noetherian ring R. We study mutation theory of 2-term silting complexes of A, and as a consequence, we see that mutation exists. As in the case of finite-dimensional algebras, functorially finite torsion classes of A bijectively correspond to silting A-modules, if R is complete local. We show a reduction theorem of 2-term silting complexes of A, and by using this theorem, we study torsion classes of the module category of A. When R has Krull dimension one, we describe the set of torsion classes of A explicitly by using the set of torsion classes of finite-dimensional algebras