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We develop silting theory of a noetherian algebra $\Lambda$ over acommutative noetherian ring $R$. We study mutation theory of $2$-term siltingcomplexes of $\Lambda$, and as a consequence, we see that mutation exists. Asin the case of finite dimensional algebras, functorially finite torsion classesof $\Lambda$ bijectively correspond to silting $\Lambda$-modules, if $R$ iscomplete local. We show a reduction theorem of $2$-term silting complexes of$\Lambda$, and by using this theorem, we study torsion classes of the modulecategory of $\Lambda$. When $R$ has Krull dimension one, we describe the set oftorsion classes of $\Lambda$ explicitly by using the set of torsion classes offinite dimensional algebras.

Tilting and silting theory of noetherian algebras