Tilting theory of noetherian algebras

Yuta Kimura

Published 2020-06-02Version 1

For a ring $\Lambda$ with a Krull-Schmidt homotopy category, we study mutation theory on $2$-term silting complexes. As a consequence, mutation works when $\Lambda$ is a complete noetherian algebra, that is, a module-finite algebra over a commutative complete local noetherian ring $R$. By using results on $2$-term silting complexes of such noetherian algebras and $\tau$-tilting theory of Artin algebras, we study torsion classes of the module category of a noetherian algebra. When $R$ has Krull dimension one, the set of torsion classes of $\Lambda$ is decomposed into subsets so that each subset bijectively corresponds to a certain subset of the set of torsion classes of Artin algebras.