相关论文: Degenerations of graded Cohen-Macaulay modules
Over-extended Kac-Moody algebras contain so-called gradient structures - a gl(d)-covariant level decomposition of the algebra contains strings of modules at different levels that can be interpreted as spatial gradients. We present an…
In Finite Group Modular Representation Theory, the basic objects are the indecomposable and simple modules. This paper offers a new classification of these objects that refines the Green Theory Classification of indecomposable and simple…
The theory of modular deformations is generalized for the category of complex analytic polyhedra which includes germs of complex space as well as any compact complex analytic space. The objective of the theory is a construction of fine…
We prove that the equivariant derived category for a finite subgroup of GL(3,C) has a semi-orthogonal decomposition into the derived category of a certain partial resolution, called a maximal Q-factorial terminalization, of the…
Let $R$ be a $G$-graded ring. In this article, we introduce two new concepts on graded rings, namely, weakly graded rings and invertible graded rings, and we discuss the relations between these concepts and several properties of graded…
Let (R,m,k) be a one-dimensional analytically unramified local ring with minimal prime ideals P_1,...,P_s. Our ultimate goal is to study the direct-sum behavior of maximal Cohen-Macaulay modules over R. Such behavior is encoded by the…
We give explicit isomorphisms between simple modules of degenerate cyclotomic Hecke algebras defined via various cellular bases. A special case gives a generalized Mullineux involution in the degenerate case.
We study commutative Cohen-Macaulay rings whose Cohen-Macaulay representation theory are controlled by representations of quivers, which we call hereditary representation type. Based on tilting theory and cluster tilting theory, we…
Let $R$ be a Cohen-Macaulay local domain. In this paper we study the cone of Cohen-Macaulay modules inside the Grothendieck group of finitely generated $R$-modules modulo numerical equivalences, introduced in \cite{CK}. We prove a result…
We show that there exists a natural non-degenerate pairing of the homomorphism space between two neighbor standard modules over a quasi-hereditary algebra with the first extension space between the corresponding costandard modules and vise…
The study of Chow varieties of decomposable forms lies at the confluence of algebraic geometry, commutative algebra, representation theory and combinatorics. There are many open questions about homological properties of Chow varieties and…
For a ringed space (X,O), we show that the deformations of the abelian category Mod(O) of sheaves of O-modules are obtained from algebroid prestacks, as introduced by Kontsevich. In case X is a quasi-compact separated scheme the same is…
We consider self-injective finite-dimensional graded algebras admitting a triangular decomposition. In a preceding paper, we have shown that the graded module category of such an algebra is a highest weight category and has tilting objects…
The category of Cohen-Macaulay modules of an algebra $B_{k,n}$ is used [JKS16] to give an additive categorification of the cluster algebra structure on the homogeneous coordinate ring of the Grassmannian of $k$-planes in $n$-space. In this…
Recent developments on the uniformity of the number of rational points on curves and subvarieties in a moving abelian variety rely on the geometric concept of the degeneracy locus. The first-named author investigated the degeneracy locus in…
We introduce and study certain deformations of Drinfeld quasi-modular forms by using rigid analytic trivialisations of corresponding Anderson's t-motives. We show that a sub-algebra of these deformations has a natural graduation by the…
In this note, we study commutative Noetherian local rings having finitely generated modules of finite Gorenstein injective dimension. In particular, we consider whether such rings are Cohen-Macaulay.
For finitely generated module $M$ over a local ring $R$, the conventional notions of complete intersection dimension $\cid_R M$ and Cohen-Macaulay dimension $\cmdim_R M$ do not extend to cover the case of infinitely generated modules. In…
We study the structural and homological properties of graded Artinian modules over generalized Weyl algebras (GWAs), and this leads to a decomposition result for the category of graded Artinian modules. Then we define and examine a category…
In this thesis, the class of modules whose Cousin complexes have finitely generated cohomologies are studied as a subclass of modules which have uniform local cohomological annihilators and it is shown that these two classes coincide over…