Silting theory under change of rings

Abstract

The main goal of this paper is to compare the silting theory of an $R$-algebra $\Lambda$ over a Noetherian ring $R$ with that of its tensor product $\Lambda \otimes \Gamma$ with another $R$-algebra $\Gamma$. In the case that the $R$-algebra $\Lambda$ is Noetherian, $R$ a complete local ring and $\mathfrak{a}$ a certain ideal of the ring $R$, we obtain an isomorphism between the silting poset of $\Lambda$ and that of its quotient $\Lambda \otimes R/ \mathfrak{a}$. Furthermore, we study the restrictions of such a bijection to tilting complexes and deduce silting embedding and descent results for the algebra $\Lambda$ and a certain family of algebras $(\Lambda \otimes \Gamma_i)_{i \in I}$.