Silting theory and derived base change

TL;DR

This paper extends the bijection between silting complexes and simple-minded collections from finite-dimensional algebras over a field to more general settings over commutative complete local noetherian rings, and explores base change properties.

Contribution

It generalizes the known bijection between silting complexes and simple-minded collections to algebras over commutative complete local noetherian rings and studies base change behavior.

Findings

Established a bijection over more general rings.

Constructed a base change bijection for silting complexes.

Generalized results to noetherian algebras.

Abstract

For finite-dimensional algebras over a field, Koenig and Yang established a bijection between silting complexes and simple-minded collections in the bounded derived category, with further contributions by many authors in various settings. In this paper, we work over a commutative complete local noetherian ring $(R,\m,k)$ rather than over a field and establish a bijection in this more general setting. As an application of this generalization, we construct a bijection between silting complexes over a noetherian $R$-algebra $\Lambda$ and silting complexes over $\Lambda\ten^\LL_RS$ for any morphism of commutative complete local noetherian rings $(R,\m,k)\to(S,\n,k)$. This result generalizes some known results on silting complexes over noetherian algebras.