Related papers: Cohen-Macaulay modules over some non-reduced curve…
We prove that certain crystabelline deformation rings of two dimensional residual representations of $\mathrm{Gal}(\overline{\mathbb{Q}}_p/\mathbb{Q}_p)$ are Cohen-Macaulay. As a consequence, this allows to improve Kisin's…
Let R be a commutative noetherian local ring. A finitely generated R-module C is semidualizing if it is self-orthogonal and satisfies the condition Hom_R(C,C) \cong R. We prove that a Cohen-Macaulay ring R with dualizing module D admits a…
In this paper we study certain category of smooth modules for reductive $p$--adic groups analogous to the usual smooth complex representations but with the field of complex numbers replaced by a $\mathbb Q$--algebra. We prove some…
We introduce and analyse a new type of quantum 2-spheres. Then we apply index theory for noncommutative line bundles over these spheres to conclude that quantum lens spaces are non-crossed-product examples of principal extensions of…
We consider integrable, category O-modules of indecomposable symmetrizable Kac-Moody algebras. We prove that unique factorization of tensor products of irreducible modules holds in this category, upto twisting by one dimensional modules.…
Let $H$ be a semisimple Hopf algebra, and let $R$ be a noetherian left $H$-module algebra. If $R/R^H$ is a right $H^*$-dense Galois extension, then the invariant subalgebra $R^H$ will inherit the AS-Cohen-Macaulay property from $R$ under…
We classify all tilting and cotilting classes over commutative noetherian rings in terms of descending sequences of specialization closed subsets of the Zariski spectrum. Consequently, all resolving subcategories of finitely generated…
We characterize Cohen-Macaulay and Gorenstein rings obtained from certain types of convex body semigroups. Algorithmic methods to check if a polygonal or circle semigroup is Cohen-Macaulay/Gorenstein are given. We also provide some families…
Noncommutative (NC) sphere is introduced as a quotient of the enveloping algebra of the Lie algebra su(2). Using the Cayley-Hamilton identities we introduce projective modules which are analogues of line bundles on the usual sphere (we call…
We study a variety for graded maximal Cohen--Macaulay modules, which was introduced by Dao and Shipman. The main result of this paper asserts that there are only a finite number of isomorphism classes of graded maximal Cohen--Macaulay…
A finitely generated module $M$ over a local ring is called a sequentially generalized Cohen-Macaulay module if there is a filtration of submodules of $M$: $M_0\subset M_1\subset ... \subset M_t=M$ such that $\dim M_0<\dim M_1< >... <\dim…
We provide two examples of smooth projective surfaces of tame CM type, by showing that any parameter space of isomorphism classes of indecomposable ACM bundles with fixed rank and determinant on a rational quartic scroll in projective…
In this paper we study Ulrich ideals of and Ulrich modules over Cohen--Macaulay local rings from various points of view. We determine the structure of minimal free resolutions of Ulrich modules and their associated graded modules, and…
For a skew version of a graded $(A_\infty)$ hypersurface singularity $A$, we study the stable category of graded maximal Cohen-Macaulay modules over $A$. As a consequence, we see that $A$ has countably infinite Cohen-Macaulay representation…
We show that, under certain constraints, the Stanley-Reisner ring of an infinite simplicial complex is Cohen-Macaulay in the sense of ideals and weak Bourbaki unmixed. We apply this result to prove the wanted claim -- that initial complexes…
Consider the special linear group of degree $2$ over an arbitrary finite field, acting on the full space of $2 \times 2$-matrices by transpose. We explicitly construct a generating set for the corresponding modular matrix invariant ring,…
Let (R,m,k) be a local Cohen-Macaulay (CM) ring of dimension one. It is known that R has finite CM type if and only if R is reduced and has bounded CM type. Here we study the one-dimensional rings of bounded but infinite CM type. We will…
The author establishes finite-generation of the cohomology ring of a classical Lie superalgebra relative to an even subsuperalgebra. A spectral sequence is constructed to provide conditions for when this relative cohomology ring is…
In this article, we show test properties, in the sense of finitely many vanishing of Ext or Tor, of CM (Cohen-Macaulay) modules whose multiplicity and number of generators (resp., type) are related by certain inequalities. We apply these…
We study the K'-theory of a CM Henselian local ring R of finite Cohen-Macaulay type. We first describe a long exact sequence involving the groups $K_i'(R)$ and the K-groups of certain other rings, including the Auslander algebra. By…