Related papers: Local duality for structured ring spectra
We introduce a local homology theory for linearly compact modules which is in some sense dual to the local cohomology theory of A. Grothendieck. Some basic properties such as the noetherianness, the vanishing and non-vanishing of local…
We consider local Gorenstein duality for cochain spectra $C^*(BG;R)$ on the classifying spaces of compact Lie groups $G$ over complex orientable ring spectra $R$. We show that it holds systematically for a large array of examples of ring…
Recently, Meierfrankenfeld has published three theorems on the cohomology of a finitary module. They cover the local determination of complete reducibility; the local splitting of group extensions; and the representation of locally split…
We present an in-depth exploration of the module structures of local (co)homology modules (moreover, for complexes) over the completion $\widehat R^{\mathfrak a}$ of a commutative noetherian ring $R$ with respect to a proper ideal…
Let R be a commutative Noetherian ring. We introduce a theory of formal local cohomology for complexes of R-modules. As an application, we establish some relations between formal local cohomology, local homology, local cohomology and local…
A duality theorem for the stable module category of representations of a finite group scheme is proved. One of its consequences is an analogue of Serre duality, and the existence of Auslander-Reiten triangles for the $\mathfrak{p}$-local…
In this paper we study local cohomology of finitely generated bigraded modules over a standard bigraded ring with respect to the irrelevant bigraded ideals and establish a duality theorem. Several applications are considered.
We discuss proofs of local cohomology theorems for topological modular forms, based on Mahowald-Rezk duality and on Gorenstein duality, and then make the associated local cohomology spectral sequences explicit, including their differential…
This paper establishes a second vanishing theorem for formal local cohomology modules over Noetherian local rings. We introduce the \textit{formal dimension} invariant and characterize the vanishing of higher formal local cohomology in…
We compute some numerical invariants of local cohomology of the ring of invariants by a finite group, mainly in the modular case. Also, we present some applications. In particular, we study Cohen-Macaulay property of modular invariants from…
In this paper, an algebraic theory for local rings of finite embedding dimension is developed. Several extensions of (Krull) dimension are proposed, which are then used to generalize singularity notions from commutative algebra. Finally,…
We introduce a concept of formal local homology modules which is in some sense dual to P. Schenzel's concept of formal local cohomology modules. The dual theorem and the non-vanishing theorem of formal local homology modules will be shown.…
In this paper, we establish the global analogues of some dualities and equivalences in local algebra by developing the theory of relative Cohen-Macaulay modules. Let R be a commutative Noetherian ring (not necessarily local) with identity…
Finitely generated reflexive modules over commutative Noetherian rings form a key component of Auslander and Bridger's stable module theory and are likewise essential in the study of Cohen--Macaulay representations. Recently, H. Dao…
In this paper we adapt the notion of the nucleus defined by Benson, Carlson, and Robinson to compact Lie groups in non-modular characteristic. We show that it describes the singularities of the projective scheme of the cohomology of its…
We investigate when a commutative ring spectrum $R$ satisfies a homotopical version of local Gorenstein duality, extending the notion previously studied by Greenlees. In order to do this, we prove an ascent theorem for local Gorenstein…
Let $R$ be a commutative Noetherian local ring. We characterize when its completion has an isolated singularity, thereby strengthening the Dao-Takahashi refinement of the Auslander-Huneke-Leuschke-Wiegand theorem. We investigate the ascent…
For the Cousin complex of certain modules, we investigate finiteness of cohomology modules, local duality property and injectivity of its terms. The existence of canonical modules of Noetherian non-local rings and the Cousin complexes of…
We generalize the completion theorem for equivariant MU-module spectra for finite groups or finite extensions of a torus to compact Lie groups using the splitting of global functors proved by Schwede. This proves a conjecture of Greenlees…
We introduce and investigate using Hilbert modules the properties of the {\em Fourier algebra} $A(G)$ for a locally compact groupoid $G$. We establish a duality theorem for such groupoids in terms of multiplicative module maps. This…