Related papers: Support and adic finiteness for complexes

We study functors underlying derived Hochschild cohomology, also called Shukla cohomology, of a commutative algebra S essentially of finite type and of finite flat dimension over a commutative noetherian ring K. We construct a complex of…

Let $\mathfrak{a}$ denote an ideal of a commutative Noetherian ring $R$. Let $M$ and $N$ be two $R$-modules. In this paper, we give partial answers on the extension of Hartshorne's conjecture about the cofiniteness of torsion and extension…

Let $R$ be a commutative Noetherian ring with non-zero identity, $\mathfrak{a}$ an ideal of $R$, $M$ a finitely generated $R$--module, and $X$ an arbitrary $R$--module. In this paper, for non-negative integers $s, t$ and a finitely…

We define objects made of marked complex disks connected by metric line segments and construct nonsymmetric and symmetric moduli spaces of these objects. This allows choices of coherent perturbations over the corresponding versions of the…

Let $\k$ be a commutative ring, and let $(A,\mfrak{a})$ be an adic ring which is a $\k$-algebra. We study complete and torsion versions of the derived Hochschild homology and cohomology functors of $A$ over $\k$. To do this, we first…

Let $A$ be a commutative noetherian ring, let $\mathfrak a$ be an ideal of $A$. In this paper, we extend Hartshorne's characterization of cofinite complexes to more general classes of rings. We also determine conditions under which…

Given a contraction of a variety X to a base Y, we enhance the locus in Y over which the contraction is not an isomorphism with a certain sheaf of noncommutative rings D, under mild assumptions which hold in the case of (1) crepant partial…

A characteristic property of cohomology with compact support is the long exact sequence that connects the compactly supported cohomology groups of a space, an open subspace and its complement. Given an arbitrary cohomology theory of…

L-modules are a combinatorial analogue of constructible sheaves on the reductive Borel-Serre compactification of a locally symmetric space. We define the micro-support of an L-module; it is a set of irreducible modules for the Levi…

For any ring $A$ and a small, preadditive, Hom-finite, and locally bounded category $Q$ that has a Serre functor and satisfies the (strong) retraction property, we show that the category of additive functors from $Q$ to the category of…

We show in this work that homology in degree d of a congruence group, in a very general framework, defines a weakly polynomial functor of degree at most 2d and we describe this functor modulo polynomial functors of smaller degree. Our main…

We develop the notion of a "filtered cospan" as an algebraic object that stands in the same relation to interlevel persistence modules as filtered chain complexes stand with respect to sublevel persistence modules. This relation is…

We advance support variety theory for finite tensor categories. First we show that the dimension of the support variety of an object equals the rate of growth of a minimal projective resolution as measured by the Frobenius-Perron dimension.…

Let $R$ be a commutative Noetherian ring and $M$ a finitely generated $R$-module. We show in this paper that, for an integer $t$, if the local cohomology module $H^{i}_\mathfrak{a}(M)$ with respect to an ideal $\frak a$ is finitely…

Let $\mathfrak{a}$ be an ideal of Noetherian ring $R$ and let $M$ be an $R$-module such that $\mathrm{Ext}^i_R(R/\mathfrak{a},M)$ is finite $R$-module for every $i$. If $s$ is the first integer such that the local cohomology module…

Let $\frak a$ be an ideal of a commutative noetherian ring $R$ with unity and $M$ an $R$-module supported at $\V(\fa)$. Let $n$ be the supermum of the integers $i$ for which $H^{\fa}_i(M)\neq 0$. We show that $M$ is $\fa$-cofinite if and…

Let $\mathfrak{a}$ be an ideal of a commutative noetherian ring $R$ and $M, N$ two finitely generated $R$-modules. By using a spectral sequence argument, it is shown that if either $\mathrm{dim}_RM\leq2$ and $\mathrm{H}^{i}_\mathfrak{a}(N)$…

We give necessary and sufficient conditions for stratification and costratification to descend along a coproduct preserving, tensor-exact $R$-linear functor between $R$-linear tensor-triangulated categories which are rigidly-compactly…

Let $R$ be commutative Noetherian ring and let $\fa$ be an ideal of $R$. For complexes $X$ and $Y$ of $R$--modules we investigate the invariant $\inf{\mathbf R}\Gamma_{\fa}({\mathbf R}\Hom_R(X,Y))$ in certain cases. It is shown that, for…

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…