Related papers: On reflexive and $I$-Ulrich modules over curve sin…

Consider a subgroup of finite index of modular group. We give an analytic criterion for a cuspidal divisor to be torsion in the Jacobian of the corresponding modular curve. By BelyI theorem, such a criterion would apply to any curve over a…

Let F be the cyclotomic field of fifth roots of unity. We computationally investigate modularity of elliptic curves over F.

In this paper, we establish the global analogues of some dualities and equivalences in local algebra by developing the theory of relative Cohen-Macaulay modules. Let R be a commutative Noetherian ring (not necessarily local) with identity…

This article concerns linear parts of minimal resolutions of finitely generated modules over commutative local, or graded rings. The focus is on the linearity defect of a module, which marks the point after which the linear part of its…

Our work is motivated by obtaining solutions to the quantum reflection equation (qRE) by categorical methods. To start, given a braided monoidal category $\mathcal{C}$ and $\mathcal{C}$-module category $\mathcal{M}$, we introduce a version…

We investigate the behavior of Cohen-Macaulay defect undertaking tensor product with a perfect module. Consequently, we study the perfect defect of a module. As an application, we connect to associated prime ideals of tensor products.

We propose a definition of Cohen--Macaulay modules over the Weyl algebra $D$ and give a sufficient condition for a GKZ $A$-hypergeometric $D$-module to be Cohen--Macaulay.

In this article we perform an extensive study of the spaces of automorphic forms for GL(2) of weight two and level N, for N an ideal in the ring of integers of the quartic CM field generated by the twelfth roots of unity. This study is…

We compute some numerical invariants of local cohomology of the ring of invariants by a finite group, mainly in the modular case. Also, we present some applications. In particular, we study Cohen-Macaulay property of modular invariants from…

This work provides a curve-based approach to Ulrich bundles on surfaces, establishing a correspondence that characterizes their existence, with a focus on applications to surfaces in $\mathbb{P}^3$.

We introduce the notion of modular $q$-holonomic modules whose fundamental matrices define a cocycle with improved analyticity properties and show that the generalised $q$-hypergeometric equation, as well as three key $q$-holonomic modules…

It is shown that a module is sequentially Cohen-Macaulay if and only if the index of reducibility for distinguished parameter ideals are eventually constant with special value. As corollaries to the main theorem we given to characterize the…

We give a theory of id\`eles with coefficients for smooth surfaces over a field. It is an analogue of Beilinson/Huber's theory of higher ad\`eles, but handling cycle module sheaves instead of quasi-coherent ones. We prove that they give a…

The present paper is the first in a series devoted to the study of asymptotic geometry of Riemann surfaces and their moduli spaces. We introduce the moduli space of hybrid curves as a new compactification of the moduli space of curves,…

Firstly, we give a partial solution to the isomorphism problem for uniserial modules of finite length with the help of the morphisms between these modules over an arbitrary ring. Later, under suitable assumptions on the lattice of the…

Let L >= 3. Using the moduli interpretation, we define certain elliptic modular forms of level Gamma(L) over any field k where 6L is invertible and k contains the Lth roots of unity. These forms generate a graded algebra R_L, which, over C,…

Unidirectional reflectionlessness is investigated in a waveguide quantum electrodynamics system that consists of a cavity and a $\Lambda$-type three-level quantum dot coupled to a one-dimensional plasmonic waveguide. Analytical expressions…

In [20] Esnault asked whether on a general quotient surface singularity the rank and the first Chern class distinguish isomorphism classes of indecomposable reflexive modules. Wunram gave a contraexample in [46] showing two different full…

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…

The cohomology algebra of the canonical bundle of a compact K\"ahler manifold is naturally viewed as a module over an exterior algebra. We use the Bernstein-Gel'fand-Gel'fand correspondence, together with Generic Vanishing theory, in order…