Related papers: Regularity of an FI-module via the derivative func…

Let $K$ be a field and let $S = K[X_1, \ldots, X_n]$. Let $I$ be a graded ideal in $S$ and let $M$ be a finitely generated graded $S$-module. We give upper bounds on the regularity of Koszul homology modules $H_i(I, M)$ for several classes…

In this article we study the local structure of the Fibonacci Partition Function by relating it to a cocycle over an irrational rotation.

Let $R$ be a ring essentially of finite type over an $F$-finite field. Given an ideal $\mathfrak{a}$ and a principal Cartier module $M$ we introduce the notion of a $V$-filtration of $M$ along $\mathfrak{a}$. If $M$ is $F$-regular then this…

We give some examples of isomorphisms of moduli of sheaves induced by Fourier-Mukai functor. As applications, we give another proof on deformation type of some moduli spaces of sheaves on abelian and K3 surfaces.

We study properties of ramification in Iwasawa modules.

We present some properties of the gradient of a mu-differentiable function. The Method of Lagrange Multipliers for mu-differentiable functions is then exemplified.

From physical perspective, derivatives can be viewed as mathematical idealizations of the linear growth. The linear growth condition has special properties, which make it preferred. The manuscript investigates the general properties of the…

Among the finitely generated modules over a Noetherian ring R, the semidualizing modules have been singled out due to their particularly nice duality properties. When R is a normal domain, we exhibit a natural inclusion of the set of…

We give a direct and elementary proof of the theorem on formal functions by studying the behaviour of the Godement resolution of a sheaf of modules under completion.

The subfactor approach to modular invariants gives insight into the fusion rule structure of the modular invariants.

Let $\mathrm{VI}$ be the category of finite dimensional $\mathbb{F}_q$-vector spaces whose morphisms are injective linear maps, and let $\mathbf{k}$ be a noetherian ring. We study the category of functors from $\mathrm{VI}$ to…

Consider a complex analytic manifold $X$ and a coherent Lie subalgebra $\shi$ of the Lie algebra of complex vector fields on $X$. By using a natural $\shd_X$-module $\shm_\shi$ naturally associated to $\shi$ and the ring (in the derived…

We construct affine algebras with an arbitrary amount of simple modules of each dimension.

Let $R$ be an associative ring with unit. Given an $R$-module $M$, we can associate the following covariant functor from the category of $R$-algebras to the category of abelian groups: $S\mapsto M\otimes_R S$. With the corresponding notion…

In this paper, we construct the motivic exceptional direct image functors for fs log schemes. This construction is a part of the motivic six-functor formalism for fs log schemes.

In this paper we introduce an inductive method to study $\mathrm{OI}$-modules presented in finite degrees, where $\mathrm{OI}$ is a skeleton of the category of finitely totally ordered sets and strictly increasing maps. As an application,…

We show that the negative-one shift functor on the category of FI-modules is a left adjoint of the shift functor and a right adjoint of the derivative functor. We also describe how the coinduction functor is related to the negative-one…

This contribution deals with identification of fractional-order dynamical systems. We consider systems whose mathematical description is a three-member differential equation in which the orders of derivatives can be real numbers. We give a…

Bounds on the Castelnuovo-Mumford regularity of the associated graded modules of k-Buchsbaum modules M are given in terms of k and some other invariants of M.

We prove maximum and comparison principles for fractional discrete derivatives in the integers. Regularity results when the space is a mesh of length $h$, and approximation theorems to the continuous fractional derivatives are shown. When…