Related papers: Stable Local Cohomology

Let $\mathcal{A}$ be a locally noetherian Grothendieck category. In this paper we define and study the section functor on $\mathcal{A}$ with respect to an open subset of ASpec$\mathcal{A}$. Next we define and study local cohomology theory…

In a preceding article the authors and Tran Ngoc Nam constructed a minimal injective resolution of the mod 2 cohomology of a Thom spectrum. A Segal conjecture type theorem for this spectrum was proved. In this paper one shows that the above…

Let $M,N$ be finitely generated modules over a local complete intersection $R$. Assume that for each $i>0$, $\mathrm{Tor}^R_i(M,N)=0$. We prove that the cohomological support of $M\otimes_R N$ (in the sense of Avramov-Buchweitz) is equal to…

Let $(A,\m)$ be a Gorenstein local ring of dimension $d \geq 1$. Let $\CMS(A)$ be the stable category of maximal \CM \ $A$-modules and let $\ICMS(A)$ denote the set of isomorphism classes in $\CMS(A)$. We define a function $\xi \colon…

For a commutative ring R and a faithfully flat R-algebra S we prove, under mild extra assumptions, that an R-module M is Gorenstein flat if and only if the left S-module S\otimes M is Gorenstein flat, and that an R-module N is Gorenstein…

We compute the stable cohomology groups of the mapping class groups of compact orientable surfaces with one boundary, with twisted coefficients given by the homology of the unit tangent bundle of the surface. This stable twisted cohomology…

Let $R$ be a finitely generated positively graded algebra over a Noetherian local ring $B$, and $\mathfrak{m} = [R]_+$ be the graded irrelevant ideal of $R$. We provide a local criterion characterizing the $B$-freeness of all the local…

Let $\frak a$, $\frak b$ be ideals of a commutative Noetherian ring $R$ and let $M$, $N$ be finite $R$-modules. The concept of an $\frak a$-filter grade of $\frak b$ on $M$ is introduced and several characterizations and properties of this…

Let $R$ be a commutative noetherian ring and $I$ an ideal of $R$. Assume that for all integers $i$ the local cohomology module $H_I^i(R)$ is $I$-cofinite. Suppose that $R_\mathfrak{p}$ is a regular local ring for all prime ideals…

As a stable analogue of degenerations, we introduce the notion of stable degenerations for Cohen-Macaulay modules over a Gorenstein local algebra. We shall give several necessary and/or sufficient conditions for the stable degeneration.…

Let $R$ be a commutative noetherian ring, and $\mathcal{Z}$ a stable under specialization subset of $\Spec(R)$. We introduce a notion of $\mathcal{Z}$-cofiniteness and study its main properties. In the case $\dim(\mathcal{Z})\leq 1$, or…

Let $\mathfrak{a}$ be an ideal of a commutative noetherian (not necessarily local) ring $R$. In the case $\cd(\mathfrak{a},R)\leq 1$, we show that the subcategory of $\mathfrak{a}$-cofinite $R$-modules is abelian. Using this and the…

We analyze stable homology over associative rings and obtain results over Artin algebras and commutative noetherian rings. Our study develops similarly for these classes; for simplicity we only discuss the latter here. Stable homology is a…

Let R be a commutative Noetherian local ring. We show that R is Gorenstein if and only if every finitely generated R-module can be embedded in a finitely generated R-module of finite projective dimension. This extends a result of Auslander…

Let $(A,\mathfrak{m})$ be an excellent equi-charateristic Gorenstein isolated singularity of dimension $d \geq 2$. Assume the residue field of $A$ is perfect. Let $I$ be any $\mathfrak{m}$-primary ideal. Let $G_I(A) = \bigoplus_{n \geq…

The paper describes a duality phenomenon for cohomology theories with the character of Gorenstein rings. For a connective cohomology theory with the p-local integers in degree 0, and coefficient ring R_* Gorenstein of shift 0, this states…

We introduce a formalism to produce several families of spectral sequences involving the derived functors of the limit and colimit functors over a finite partially ordered set. The first type of spectral sequences involves the left derived…

It is proved that the minimal free resolution of a module M over a Gorenstein local ring R is eventually periodic if, and only if, the class of M is torsion in a certain Z[t,t^{-1}]-module associated to R. This module, denoted J(R), is the…

Let $R$ be a commutative Noetherian ring, and let $\mathfrak a$ be a proper ideal of $R$. Let $M$ be a non-zero finitely generated $R$-module with the finite projective dimension $p$. Also, let $N$ be a non-zero finitely generated…

Let ($S, \mathfrak{n})$ be a commutative noetherian local ring and let $\omega\in\mathfrak{n}$ be non-zero divisor. This paper is concerned with the category of monomorphisms between finitely generated Gorenstein projective S-modules, such…