Compactly generated t-structures in the derived category of a commutative ring

TL;DR

This paper classifies all compactly generated t-structures in the derived category of any commutative ring, extending previous results for noetherian rings and establishing a correspondence with filtrations of the spectrum.

Contribution

It generalizes the classification of t-structures to arbitrary commutative rings and links them to spectral filtrations, also classifying cosilting complexes.

Findings

Bijective correspondence between t-structures and spectral filtrations.

All cosilting complexes are classified up to equivalence.

In noetherian case, all bounded below homotopically smashing t-structures are compactly generated.

Abstract

We classify all compactly generated t-structures in the unbounded derived category of an arbitrary commutative ring, generalizing the result of [ATLJS10] for noetherian rings. More specifically, we establish a bijective correspondence between the compactly generated t-structures and infinite filtrations of the Zariski spectrum by Thomason subsets. Moreover, we show that in the case of a commutative noetherian ring, any bounded below homotopically smashing t-structure is compactly generated. As a consequence, all cosilting complexes are classified up to equivalence.