Bounded t-structures on the category of perfect complexes over a Noetherian ring of finite Krull dimension

TL;DR

This paper classifies bounded t-structures on perfect complexes over Noetherian rings of finite Krull dimension, confirming conjectures about their existence in singular cases and extending previous results beyond regular rings.

Contribution

It extends the classification of bounded t-structures to singular Noetherian rings, proving their non-existence in certain singular cases and confirming conjectures.

Findings

No bounded t-structures in singular cases

No non-trivial t-structures in singular, irreducible cases

Extension of classification results beyond regular rings

Abstract

We classify bounded t-structures on the category of perfect complexes over a commutative, Noetherian ring of finite Krull dimension, extending a result of Alonso Tarrio, Jeremias Lopez and Saorin which covers the regular case. In particular, we show that there are no bounded t-structures in the singular case, verifying the affine version of a conjecture of Antieau, Gepner and Heller, and also that there are no non-trivial t-structures at all in the singular, irreducible case.