Related papers: Local duality for structured ring spectra

Let E=BP<n> denote the Johnson-Wilson spectrum, localized at p. It is proved that if E_*(X) is locally finite, then there is an isomorphism of right E_*-modules E^*(X) = (E_*(Sigma^{D+n+1}X))^V, where D=Sum |v_i| and M^V=Hom(M,Q/Z) is the…

We propose a new method for defining a notion of support for objects in any compactly generated triangulated category admitting small coproducts. This approach is based on a construction of local cohomology functors on triangulated…

We give a refinement of Saito's arithmetic duality for two-dimensional local rings by giving algebraic group structures for arithmetic cohomology groups.

We introduce the notion of a contramodule over a cocommutative coalgebra in a presentably symmetric monoidal $\infty$-category $\mathcal{C}$, and prove a symmetric monoidal $\infty$-categorical version of Positselski's comodule-contramodule…

We develop a formalism of unit $F$-modules in the style of Lyubeznik and Emerton-Kisin for rings which have finite $F$-representation type after localization and completion at every prime ideal. As applications, we show that if $R$ is such…

Cohen-Macaulay dimension for modules over a commutative noetherian local ring has been defined by A. A. Gerko. That is a homological invariant sharing many properties with projective dimension and Gorenstein dimension. The main purpose of…

Rational discrete cohomology and homology for a totally disconnected locally compact group $G$ is introduced and studied. The $\mathrm{Hom}$-$\otimes$ identities associated to the rational discrete bimodule $\mathrm{Bi}(G)$ allow to…

We provide a formula (see Theorem 1.5) for the Matlis dual of the injective hull of $R/\mathfrak{p}$ where $\mathfrak p$ is a one dimensional prime ideal in a local complete Gorenstein domain $(R,\mathfrak{m})$. This is related to results…

Let $\fa$ be an ideal of a Noetherian local ring $R$ and let $C$ be a semidualizing $R$-module. For an $R$-module $X$, we denote any of the quantities $\fd_R X$, $\Gfd_R X$ and $\GCfd_RX$ by $\T(X)$. Let $M$ be an $R$-module such that…

In this note, some properties of finitely generated two-periodic modules over commutative Noetherian local rings have been studied. We show that under certain assumptions on a pair of modules $\left(M,N \right)$ with $M$ two-periodic, the…

We define and study the invariant linear and nonlinear horizontal double complexes of a local Lie group.

In this paper some applications of the methods and results of its first part and of the results of M. Stone, H. de Vries, P. Roeper are given. In particular: some generalizations of the Stone Duality Theorem are obtained; a completion…

Let $J$ be an ideal of a noetherian local ring $R$. We show new results on the set of attached primes $\Att_R(\LCMo ^l_J(R))$ of a local cohomology module $\LCMo ^l_J(R)$. To prove our results we establish and use new relations between the…

Let $R$ be a Noetherian ring and let $C$ be a semidualizing $R$-module. In this paper, by using the classes $ \mathcal{P}_C $ and $ \mathcal{I}_C $, we extend the notions of perfect and coperfect modules introduced by D.Rees \cite{R} and…

We use our extension of the Noether-Lefschetz theorem to describe generators of the class groups at the local rings of singularities of very general hypersurfaces containing a fixed base locus. We give several applications, including (1)…

We give several related versions of global Grothendieck Duality for unbounded complexes on noetherian formal schemes. The proofs, based on a non-trivial adaptation of Deligne's method for the special case of ordinary schemes, are reasonably…

Considering modules of finite complete intersection dimension over commutative Noetherian local rings, we prove (co)homology vanishing results in which we assume the vanishing of nonconsecutive (co)homology groups. In fact, the (co)homology…

In this note ($R, m$) denotes a complete regular local ring and $B$ mostly denotes its absolute integral closure. The four objectives of this paper are the following: i) to determine the highest non-vanishing local cohomology of…

We extend the duality theory for topological groups from the classical theory for compact Lie groups, via the topological study by J. R. Klein [Kl01] and the p-complete study for p-compact groups by T. Bauer [Ba04], to a general duality…

Gross and Hopkins have proved that in chromatic stable homotopy, Spanier-Whitehead duality nearly coincides with Brown-Comenetz duality. Our goal is to give a conceptual interpretation for this phenomenon in terms of the Gorenstein…