Silting, cosilting, and extensions of commutative ring

TL;DR

This paper investigates how silting and cosilting objects in derived categories behave under ring extensions, showing preservation and descent properties, and establishing the Zariski locality of bounded silting complexes.

Contribution

It demonstrates that extension functors preserve (co)silting objects of finite type and that bounded silting complexes are Zariski local, advancing understanding of their behavior under ring extensions.

Findings

Extension functors preserve (co)silting objects of finite type

Bounded silting property descends along faithfully flat extensions

Bounded silting complexes are Zariski local

Abstract

We study the transfer of (co)silting objects in derived categories of module categories via the extension functors induced by a morphism of commutative rings. It is proved that the extension functors preserve (co)silting objects of (co)finite type. In many cases the bounded silting property descends along faithfully flat ring extensions. In particular, the notion of bounded silting complex is Zariski local.