Related papers: Some families of non-isomorphic maximal function f…

An independent set $I$ in a graph $G$ is maximal if $I$ is not properly contained in any other independent set of $G$. The study of maximal independent sets (MIS's) in various graphs is well-established, often focusing upon enumeration of…

In this note, we consider function fields of higher-dimensional algebraic varieties defined over non-local fields, and show how the Galois action on the cohomology such function fields can be used to parameterize their divisorial…

We show that a finite-dimensional tame division algebra D over a Henselian field F has a maximal subfield Galois over F if and only if its residue division algebra has a maximal subfield Galois over the residue field of F. This generalizes…

We consider the well-known Rosenbloom-Tsfasman function field lattices in the special case of Hermitian function fields. We show that in this case the resulting lattices are generated by their minimal vectors, provide an estimate on the…

For an algebraically closed field K, let G be a finite abelian group of K-linear automorphisms of a finite-dimensional path algebra KQ of a quiver Q. Under certain assumptions on the action of G, we show the existence of a certain kind of…

Let F be a finitely generated field of characteristic zero and \Gamma<GL_n(F) a finitely generated subgroup. For an element g in \Gamma, let Gal(F(g)/ F) be the Galois group of the splitting field of the characteristic polynomial of g over…

In the framework of algebraic quantum field theory we analyze the anomalous statistics exhibited by a class of automorphisms of the observable algebra of the two-dimensional free massive Dirac field, constructed by fermionic gauge group…

For every $q=n^3$ with $n$ a prime power greater than $2$, the GK-curve is an $\mathbb F_{q^2}$-maximal curve that is not $\mathbb F_{q^2}$-covered by the Hermitian curve. In this paper some Galois subcovers of the GK curve are…

We show that any Lambda-ring, in the sense of Riemann-Roch theory, which is finite etale over the rational numbers and has an integral model as a Lambda-ring is contained in a product of cyclotomic fields. In fact, we show that the category…

In this paper we define a pair of faithful functors that map isomorphic and isotopic finite-dimensional algebras over finite fields to isomorphic graphs. These functors reduce the cost of computation that is usually required to determine…

We present a Galois theory of parameterized linear differential equations where the Galois groups are linear differential algebraic groups, that is, groups of matrices whose entries are functions of the parameters and satisfy a set of…

A description of group automorphisms of all two-dimensional algebras, considered up to isomorphism, over any basic field is provided.

This paper studies the uniqueness of two non-constant meromorphic functions when they share a finite set. Moreover, we will give the existence of unique range sets for meromorphic functions that are zero sets of polynomials that do not…

We study ``forms of the Fermat equation'' over an arbitrary field $k$, i.e. homogenous equations of degree $m$ in $n$ unknowns that can be transformed into the Fermat equation $X_1^m+...+X_n^m$ by a suitable linear change of variables over…

In this paper we construct Galois towers with good asymptotic properties over any non-prime finite field $\mathbb F_{\ell}$; i.e., we construct sequences of function fields $\mathcal{N}=(N_1 \subset N_2 \subset \cdots)$ over $\mathbb…

The absolute Galois group of the cyclotomic field $K={\mathbb Q}(\zeta_p)$ acts on the \'etale homology of the Fermat curve $X$ of exponent $p$. We study a Galois cohomology group which is valuable for measuring an obstruction for…

We study the minimal number of ramified primes in Galois extensions of rational function fields over finite fields with prescribed finite Galois group. In particular, we obtain a general conjecture in analogy with the well studied case of…

Some sorts of generalized morphisms are defined from very basic mathematical objects such as sets, functions, and partial functions. A wide range of mathematical notions such as continuous functions between topological spaces, ring…

We compare two classes of functions arising from genus-one superstring amplitudes: modular and holomorphic graph functions. We focus on their analytic properties, we recall the known asymptotic behaviour of modular graph functions and we…

This paper is a survey, with few proofs, of ideas and notions related to self-similarity of groups, semi-groups and their actions. It attempts to relate these concepts to more familiar ones, such as fractals, self-similar sets, and…