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

M Hrbek - Mathematische Zeitschrift, 2020 - Springer
We classify all compactly generated t-structures in the unbounded derived category of an
arbitrary commutative ring, generalizing the result of Alonso Tarrío et al.(J Algebra 324 (3) …

Hearts of t-structures in the derived category of a commutative Noetherian ring

C Parra, M Saorin - Transactions of the American Mathematical Society, 2017 - ams.org
Let $ R $ be a commutative Noetherian ring and let $\mathcal D (R) $ be its (unbounded)
derived category. We show that all compactly generated t-structures in $\mathcal D (R) …

Parametrizing torsion pairs in derived categories

L Angeleri Hügel, M Hrbek - … Theory of the American Mathematical Society, 2021 - ams.org
We investigate parametrizations of compactly generated t-structures, or more generally, t-
structures with a definable coaisle, in the unbounded derived category $\mathrm …

Telescope conjecture for homotopically smashing t-structures over commutative noetherian rings

M Hrbek, T Nakamura - Journal of Pure and Applied Algebra, 2021 - Elsevier
We show that any homotopically smashing t-structure in the derived category of a
commutative noetherian ring is compactly generated. This generalizes the validity of the …

t-Structures and cotilting modules over commutative noetherian rings

L Angeleri Hügel, M Saorín - Mathematische Zeitschrift, 2014 - Springer
For a commutative noetherian ring\(R\), we establish a bijection between the resolving
subcategories consisting of finitely generated\(R\)-modules of finite projective dimension …

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

H Smith - Advances in Mathematics, 2022 - Elsevier
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 Tarrío, Jeremías López …

Gluing compactly generated t-structures over stalks of affine schemes

M Hrbek, J Hu, R Zhu - Israel Journal of Mathematics, 2024 - Springer
We show that compactly generated t-structures in the derived category of a commutative ring
R are in a bijection with certain families of compactly generated t-structures over the local …

Invariants of t-structures and classification of nullity classes

D Stanley - Advances in Mathematics, 2010 - Elsevier
We construct an invariant of t-structures on the derived category of a commutative
noetherian ring. This invariant is complete when restricting to the category of complexes with …

Compactly generated t-structures on the derived category of a Noetherian ring

LA Tarrío, AJ López, M Saorín - Journal of Algebra, 2010 - Elsevier
We study t-structures on D (R) the derived category of modules over a commutative
Noetherian ring R generated by complexes in Dfg−(R). We prove that they are exactly the …

On compactly generated torsion pairs and the classification of co-𝑡-structures for commutative noetherian rings

J Šťovíček, D Pospíšil - Transactions of the American Mathematical Society, 2016 - ams.org
We classify compactly generated co-$ t $-structures on the derived category of a
commutative noetherian ring. In order to accomplish this, we develop a theory for compactly …