The ascent-descent property for $2$-term silting complexes

TL;DR

This paper investigates how the silting property of 2-term complexes over commutative rings behaves under faithfully flat extensions, establishing preservation and reflection properties.

Contribution

It proves that the silting property of 2-term complexes induced by morphisms between projective modules is preserved and reflected by faithfully flat extensions over commutative rings.

Findings

Silting property is preserved under faithfully flat extensions.

Silting property is reflected by faithfully flat extensions.

Results apply to complexes induced by morphisms between projective modules.

Abstract

We will prove that over commutative rings the silting property of $2$-term complexes induced by morphisms between projective modules is preserved and reflected by faithfully flat extensions.