Related papers: A Carlitz module analogue of the Grunwald--Wang th…

Let $p$ be a prime and let $G$ be a finite group. By a celebrated theorem of Swan, two finitely generated projective $\mathbb Z_p[G]$-modules $P$ and $P'$ are isomorphic if and only if $\mathbb Q_p \otimes_{\mathbb Z_p} P$ and $\mathbb Q_p…

Let $\Gamma$ be a finite d-valent graph and G an n-dimensional torus. An ``action'' of G on $\Gamma$ is defined by a map, $\alpha$, which assigns to each oriented edge e of $\Gamma$ a one-dimensional representation of G (or, alternatively,…

Global Weyl modules for generalized loop algebras $\lie g\tensor A$, where $\lie g$ is a simple finite dimensional Lie algebra and A is a commutative associative algebra were defined, for any dominant integral weight $\lambda$, by…

We introduce a new type of convergence in probability theory, which we call ``mod-Gaussian convergence''. It is directly inspired by theorems and conjectures, in random matrix theory and number theory, concerning moments of values of…

A well-known theorem of Kaplansky states that any projective module is a direct sum of countably generated modules. In this paper, we prove the $w$-version of this theorem, where $w$ is a hereditary torsion theory for modules over a…

We present a quick approach to computing the $K$-theory of the category of locally compact modules over any order in a semisimple $\mathbb{Q}$-algebra. We obtain the $K$-theory by first quotienting out the compact modules and subsequently…

We study Hom-quantum groups, their representations, and module Hom-algebras. Two Twisting Principles for Hom-type algebras are formulated, and construction results are proved following these Twisting Principles. Examples include Hom-quantum…

In this paper, we study a density version of the Waring-Goldbach problem. Suppose that A is a subset of the primes, and the lower density of A in the primes is larger than 1-1/2k. We prove that every sufficiently large natural number n…

In this article we give an analogue of Hecke and Sturm bounds for Hilbert modular forms over real quadratic fields. Let $K$ be a real quadratic field and $\Om_K$ its ring of integers. Let $\Gamma$ be a congruence subgroup of $\SL_2(\Om_K)$…

We provide and study an equivariant theory of group (co)homology of a group G with coefficients in a gamma-equivariant G-module A, when a separate group "gamma" acts on G and A, generalizing the classical Eilenberg-MacLane (co)homology of…

A natural number is a binary $k$'th power if its binary representation consists of $k$ consecutive identical blocks. We prove an analogue of Waring's theorem for sums of binary $k$'th powers. More precisely, we show that for each integer $k…

Given a finite group $G$ and a number field $K$, we investigate the following question: Does there exist a Galois extension $E/K(t)$ with group $G$ whose set of specializations yields solutions to all Grunwald problems for the group $G$,…

Let $(F,J,\omega)$ be an almost K\"ahler manifold, $\alpha$ a $J$-holomorphic action of a compact Lie group $\hat K$ on $F$, and $K$ a closed normal subgroup of $\hat K$ which leaves $\omega$ invariant. We introduce gauge theoretical…

In this paper we investigate a local to global principle for Mordell-Weil group defined over a ring of integers ${\cal O}_K$ of $t$-modules that are products of the Drinfeld modules ${\widehat\varphi}={\phi}_{1}^{e_1}\times \dots \times…

Given a number field $k$ with the ring of integers $\mathcal{O}_k$ and a matrix $M\in \mathrm{M}_{n}(\mathcal{O}_k)$. We prove that if $\mathcal{O}_k$ is a principal ideal domain, the local-global principle for triangularizability and…

In this paper, we introduce a Carlitz module analogue of Mersenne primes, and prove Carlitz module analogues of several classical results concerning Mersenne primes. In contrast to the classical case, we can show that there are infinitely…

Recently the second author has associated a finite $\F_q[T]$-module $H$ to the Carlitz module over a finite extension of $\F_q(T)$. This module is an analogue of the ideal class group of a number field. In this paper we study the Galois…

We analyze the "F-locality condition" (proposed by Kay to be a mathematical implementation of a philosophical bias related to the equivalence principle, we call it the "GH-equivalence principle"), which is often used to build a…

We introduce k-quantifier logics -- logics with access to k-tuples of elements and very general quantification patterns for transitions between k-tuples. The framework is very expressive and encompasses e.g. the k-variable fragments of…

A conjecture of Hirschowitz's predicts that a globally generated vector bundle $W$ on a compact complex manifold $A$ satisfies the formal principle, i.e., the formal neighborhood of its zero section determines the germ of neighborhoods in…