Related papers: Strongly residual coordinates over A[x]

The aim of this note is to construct sequences of vector bundles with unbounded rank and discriminant on an arbitrary algebraic surface. This problem, on principally polarized abelian varieties with cyclic Neron-Severi group generated by…

Given a polynomial P in several variables over an algebraically closed field, we show that except in some special cases that we fully describe, if one coefficient is allowed to vary, then the polynomial is irreducible for all but at most…

Representations of vertex operator algebras $V$ (VOAs) have numerous applications, including the construction of sheaves of conformal blocks on moduli spaces of curves. For a $V$-module $W = \oplus W_d$, a sequence of associative algebras…

In many matching markets--such as athlete recruitment or academic admissions--participants on one side are evaluated by attribute vectors known to the other side, which in turn applies individual \emph{salience vectors} to assign relative…

For a class of polynomials $f \in \mathbb{Z}[X]$, which in particular includes all quadratic polynomials, and also trinomials of some special form, we show that, under some natural conditions (necessary for quadratic polynomials), the set…

Polynomial completeness results aim at characterizing those functions that are induced by polynomials. Each polynomial function is congruence preserving, but the opposite need not be true. A finite algebraic structure $\mathbf{A}$ is called…

Suppose M is a complex manifold of dimension $n+1$ and K is a hypersurface in M. By Poincar\'e duality we define a residue morphism $res:H^{k+1}(M\setminus K)\longrightarrow H_{2n-k}(K)$ which generalizes the classical Leray residue…

Let $k$ be a perfect field of characteristic $p >0$, $U$ be a variety over $k$ and $F$ be a power of Frobenius. We construct the category of overholonomic arithmetical ($F$-)$\D$-modules over $U$ and the category of overholonomic…

We discuss several conjectures about the real-rootedness of polynomials whose coefficients are determinants of coefficients of a real-rooted polynomial. We also consider some questions about matrices generalizing totally positive matrices,…

A subshift on a group G is a closed, G-invariant subset of A^G, for some finite set A. It is said to be a subshift of finite type (SFT) if it is defined by a finite collection of 'forbidden patterns', to be strongly aperiodic if all point…

Let $\mathbb{F}_q$ be a finite field with $q$ elements and denote by $\theta : \mathbb{F}_q\to\mathbb{F}_q$ an automorphism of $\mathbb{F}_q$. In this paper, we deal with skew constacyclic codes, that is, linear codes of $\mathbb{F}_q^n$…

A differential algebra of finite type over a field k is a filtered algebra A, such that the associated graded algebra is finite over its center, and the center is a finitely generated k-algebra. The prototypical example is the algebra of…

We study connections between self-inversive and self-reciprocal polynomials, reduction theory of binary forms, minimal models of curves, and formally self-dual codes. We prove that if $\mathcal X$ is a superelliptic curve defined over…

Let S be an infinite set of non-empty, finite subsets of the nonnegative integers. If p is an odd prime, let c(p) denote the cardinality of the set {T {\in} S : T {\subseteq} {1,...,p-1} and T is a set of quadratic residues (respectively,…

This paper investigates the effective categoricity of ultrahomogeneous structures. It is shown that any computable ultrahomogeneous structure is $\Delta^0_2$ categorical. A structure A is said to be weakly ultrahomogeneous if there is a…

Let R be a Dedekind domain with global quotient field K. The purpose of this note is to provide a characterization of when a strongly graded R-order with semiprime 1-component is hereditary. This generalizes earlier work by the first author…

Let $X$ be an inner product space, let $G$ be a group of orthogonal transformations of $X$, and let $R$ be a bounded $G$-stable subset of $X$. We define very weak and very strong regularity for such pairs $(R,G)$ (in the sense of…

Symmetric strongly shifted ideals are a class of monomial ideals which come equipped with an action of the symmetric group and are analogous to the well-studied class of strongly stable monomial ideals. In this paper we focus on algebraic…

Let $L$ be a differential operator with coefficients in $\mathbb{Q}(z)$ of order $n\geq2$ with maximal unipotent monodromy at zero. In this paper we are interested in determining when the canonical coordinate of $L$ belongs to…

We show that Out(G) is residually finite if G is a one-ended group that is hyperbolic relative to virtually polycyclic subgroups. More generally, if G is one-ended and hyperbolic relative to proper residually finite subgroups, the group of…