[HTML][HTML] Minimal semi-flat-cotorsion replacements and cosupport
T Nakamura, P Thompson - Journal of Algebra, 2020 - Elsevier
Over a commutative noetherian ring R of finite Krull dimension, we show that every complex
of flat cotorsion R-modules decomposes as a direct sum of a minimal complex and a …
of flat cotorsion R-modules decomposes as a direct sum of a minimal complex and a …
Flat cotorsion modules over Noether algebras
R Kanda, T Nakamura - Documenta Mathematica, 2022 - ems.press
For a module-finite algebra over a commutative noetherian ring, we give a complete
description of flat cotorsion modules in terms of prime ideals of the algebra, as a …
description of flat cotorsion modules in terms of prime ideals of the algebra, as a …
Pure-minimal chain complexes
LW Christensen, P Thompson - Rendiconti del Seminario Matematico …, 2019 - ems.press
We introduce a notion of pure-minimality for chain complexes of modules and show that it
coincides with (homotopic) minimality in standard settings, while being a more useful notion …
coincides with (homotopic) minimality in standard settings, while being a more useful notion …
Localization functors and cosupport in derived categories of commutative Noetherian rings
T Nakamura, Y Yoshino - Pacific Journal of Mathematics, 2018 - msp.org
Let R be a commutative Noetherian ring. We introduce the notion of localization functors λ W
with cosupports in arbitrary subsets W of Spec R; it is a common generalization of …
with cosupports in arbitrary subsets W of Spec R; it is a common generalization of …
[HTML][HTML] Cosupport computations for finitely generated modules over commutative noetherian rings
P Thompson - Journal of Algebra, 2018 - Elsevier
We show that the cosupport of a commutative noetherian ring is precisely the set of primes
appearing in a minimal pure-injective resolution of the ring. As an application of this, we …
appearing in a minimal pure-injective resolution of the ring. As an application of this, we …
[HTML][HTML] Duality between injective envelopes and flat covers
V Puuska - Journal of Pure and Applied Algebra, 2024 - Elsevier
We establish a duality between injective envelopes and flat covers over a commutative
Noetherian ring. One case of this duality states that a morphism is an injective envelope, if …
Noetherian ring. One case of this duality states that a morphism is an injective envelope, if …
[HTML][HTML] Cosupports and minimal pure-injective resolutions of affine rings
T Nakamura - Journal of Algebra, 2019 - Elsevier
We prove that any affine ring R over a field k has full cosupport, ie, the cosupport of R is
equal to Spec R. Using this fact, we give a complete description of all terms in a minimal …
equal to Spec R. Using this fact, we give a complete description of all terms in a minimal …
Rigidity of Ext and Tor via flat–cotorsion theory
LW Christensen, L Ferraro… - Proceedings of the …, 2023 - cambridge.org
Let. This improves a result of Christensen, Iyengar and Marley by lowering the bound on n.
We also improve existing results on Tor-rigidity. This progress is driven by the existence of …
We also improve existing results on Tor-rigidity. This progress is driven by the existence of …
[PDF][PDF] Localization and colocalization in derived categories
T Nakamura - 2018 - ousar.lib.okayama-u.ac.jp
In the 1960s, Grothendieck introduced the notion of local cohomology from the viewpoint of
geometry. It has brought great benefits to commutative algebra, and has been an essential …
geometry. It has brought great benefits to commutative algebra, and has been an essential …