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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …