Paper detail

Silting theory under change of rings

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