On silting complexes associated to n-silting modules

TL;DR

This paper establishes a connection between (n+1)-term silting complexes and n-silting modules, especially over commutative noetherian rings, and explores their relation to tilting complexes and t-structures.

Contribution

It demonstrates that certain silting complexes induce n-silting modules and shows a bijection between their equivalence classes in commutative noetherian rings, also linking to tilting complexes.

Findings

(n+1)-term silting complexes yield n-silting modules when intermediate cohomology vanishes

The assignment induces a bijection on equivalence classes over commutative noetherian rings

n-silting modules correspond to tilting complexes with derived type t-structures

Abstract

We show that any (n+1)-term silting complex whose intermediate cohomology vanishes gives rise to an n-silting module, as recently introduced by Mao. Specializing to commutative noetherian rings, we show that this assignment induces a bijection on the respective equivalence classes. Furthermore, we prove in the same setting that the n-silting modules always correspond to a tilting complex, that is, the associated t-structure is of derived type. We use this to exhibit new examples of tilting complexes in the setting of Commutative Algebra and also to show that the finite type property for n-silting modules, as formulated by Mao, can in general fail.