Tilting and silting theory of noetherian algebras

Abstract

We develop silting theory of a noetherian algebra $\Lambda$ over a commutative noetherian ring $R$. We study mutation theory of $2$-term silting complexes of $\Lambda$, and as a consequence, we see that mutation exists. As in the case of finite dimensional algebras, functorially finite torsion classes of $\Lambda$ bijectively correspond to silting $\Lambda$-modules, if $R$ is complete local. We show a reduction theorem of $2$-term silting complexes of $\Lambda$, and by using this theorem, we study torsion classes of the module category of $\Lambda$. When $R$ has Krull dimension one, we describe the set of torsion classes of $\Lambda$ explicitly by using the set of torsion classes of finite dimensional algebras.