Singular equivalences to locally coherent hearts of commutative noetherian rings
M Hrbek, S Pavon - Journal of Algebra, 2023 - Elsevier
We show that Krause's recollement exists for any locally coherent Grothendieck category
whose derived category is compactly generated. As a source of such categories, we …
whose derived category is compactly generated. As a source of such categories, we …
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) …
derived category. We show that all compactly generated t-structures in $\mathcal D (R) …
Hearts for commutative Noetherian rings: torsion pairs and derived equivalences
S Pavon, J Vitória - Documenta Mathematica, 2021 - content.ems.press
Over a commutative noetherian ring R, the prime spectrum controls, via the assignment of
support, the structure of both Mod (R) and D (R). We show that, just like in Mod (R), the …
support, the structure of both Mod (R) and D (R). We show that, just like in Mod (R), the …
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 …
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 …
subcategories consisting of finitely generated\(R\)-modules of finite projective dimension …
Complete intersections and derived categories
DJ Benson, JPC Greenlees - arXiv preprint arXiv:0906.4025, 2009 - arxiv.org
We propose a definition of when a triangulated category should be considered a complete
intersection. We show (using work of Avramov and Gulliksen) that for the derived category of …
intersection. We show (using work of Avramov and Gulliksen) that for the derived category of …
Bounded derived categories of infinite quivers: Grothendieck duality, reflection functor
J Asadollahi, R Hafezi, R Vahed - Canadian Journal of Mathematics, 2015 - cambridge.org
We study bounded derived categories of the category of representations of infinite quivers
over a ring is a commutative noetherian ring with a dualising complex, we investigate an …
over a ring is a commutative noetherian ring with a dualising complex, we investigate an …
[PDF][PDF] Generators in Grothendieck categories with right perfect endomorphism rings
T Albu, R Wisbauer - 1991 - projecteuclid.org
It is well-known that Grothendieck categories need not have projective objects (eg [12],
18.12). However, projective objects can be obtained from certain finiteness conditions. By a …
18.12). However, projective objects can be obtained from certain finiteness conditions. By a …
On locally coherent hearts
M Saorín - Pacific Journal of Mathematics, 2017 - msp.org
Let G be a locally coherent Grothendieck category. We show that, under particular
conditions, if a t-structure τ in the unbounded derived category D (G) restricts to the bounded …
conditions, if a t-structure τ in the unbounded derived category D (G) restricts to the bounded …
Grothendieck groups and tilting objects
I Reiten, M Van den Bergh - Algebras and representation theory, 2001 - Springer
Let C be a connected Noetherian hereditary Abelian category with a Serre functor over an
algebraically closed field k, with finite-dimensional homomorphism and extension spaces …
algebraically closed field k, with finite-dimensional homomorphism and extension spaces …