Related papers: On Cohen--Macaulay modules over the Weyl algebra

We prove a duality theorem for Cohen--Macaulay simplicial complexes. This is a generalisation of Poincar\'e Duality, framed in the language of combinatorial sheaves. Our treatment is self-contained and accessible for readers with a working…

In this paper we aim to understand the category of stable-Yetter-Drinfeld modules over enveloping algebra of Lie algebras. To do so, we need to define such modules over Lie algebras. These two categories are shown to be isomorphic. A mixed…

We will describe the Cohen--Macaulay part of the Ziegler spectrum of the D-infinity plane singularity S and calculate the nilpotency index of the radical of the category of finitely generated Cohen--Macaulay S-modules.

In its most basic form, Dubreil's Theorem states that for an ideal $I$ defining a codimension $2$, arithmetically Cohen--Macaulay subscheme of projective $n$-space, the number of generators of $I$ is bounded above by the minimal degree of a…

We give a necessary condition of degeneration via matrix representations, and consider degenerations of indecomposable Cohen-Macaulay modules over hypersurface singularities of type ($A_\infty$). We also provide a method to construct…

Let R be a commutative Noetherian ring, a a proper ideal of R and M a finite R-module. It is shown that, if (R;m) is a complete local ring, then under certain conditions a contains a regular element on DR(Hc a(M)), where c = cd(a;M). A…

Over a Cohen-Macaulay (CM) local ring, we characterize those modules that can be obtained as a direct limit of finitely generated maximal CM modules. We point out two consequences of this characterization: (1) Every balanced big CM module,…

Let $(A,\mathfrak{m})$ be a Henselian Cohen-Macaulay local ring and let CM(A) be the category of maximal Cohen-Macaulay $A$-modules. We construct $T \colon CM(A)\times CM(A) \rightarrow mod(A)$, a subfunctor of $Ext^1_A(-, -)$ and use it to…

If $A$ is a subset of the set of reflections of a finite Coxeter group $W$, we define a sub-${\mathbb{Z}}$-module ${\mathcal{D}}_A(W)$ of the group algebra ${\mathbb{Z}} W$. We provide examples where this submodule is a subalgebra. This…

Let $R$ be a polynomial ring over a field. We introduce the concept of sequentially almost Cohen-Macaulay modules and describe the extremal rays of the cone of local cohomology tables of finitely generated graded $R$-modules which are…

Given a germ of holomorphic map $f$ from $\mathbb C^n$ to $\mathbb C^{n+1}$, we define a module $M(f)$ whose dimension over $\mathbb C$ is an upper bound for the $\mathscr A$-codimension of $f$, with equality if $f$ is weighted homogeneous.…

By extending some basic results of Grothendieck and Foxby about local cohomology to commutative DG-rings, we prove new amplitude inequalities about finite DG-modules of finite injective dimension over commutative local DG-rings,…

The purpose of this paper is to develop a new theory of gauges in mixed characteristic. Namely, let $k$ be a perfect field of characteristic $p>0$ and $W(k)$ the $p$-typical Witt vectors. Making use of Berthelot's arithmetic differential…

We study the category of modules of minimal dimension over completed Weyl algebras in equal characteristic zero. In particular we prove finiteness of de Rham cohomology of such modules.

Let $M$ be a finitely generated module of dimension $d$ over a Noetherian local ring $(R,\m)$ and $\q $ the parameter ideal generated by a system of parameters $\x = (x_1,..., x_d)$ of $M$. For each positive integer $n$, set…

In this paper, we study maximal Cohen-Macaulay sheaves on closures of minimal nilpotent orbits in simple Lie algebras. For singularities of type $A_n$, we first classify vector bundles on their symplectic resolutions whose pushforwards are…

We shall show that the stable categories of graded Cohen-Macaulay modules over quotient singularities have tilting objects. In particular, these categories are triangle equivalent to derived categories of finite dimensional algebras. Our…

We define Weyl functors, global modules for equivariant map Lie superalgebras $(\g \otimes A)^{\Gamma}$, where $\g$ is basic classical $\mathbb{C}$- Lie superalgebra and $A$ is an associative commutative unital $\mathbb{C}$-algebra. Under…

We present a simple method for determining the shape of fundamental domains of generalized modular groups related to Weyl groups of hyperbolic Kac-Moody algebras. These domains are given as subsets of certain generalized upper half planes,…

Every quotient R/I of a semigroup ring R by a radical monomial ideal I has a unique minimal injective-like resolution by direct sums of quotients of R modulo prime monomial ideals. The quotient R/I is Cohen-Macaulay if and only if every…