Franccois Legrand

activity

20112023

most citedA note on finite embedding problems with nilpotent kernel

1 citations · 1 across the 7 of their papers we have counts for

collaborators

10 papers

math.NT2023

Lüroth's and Igusa's theorems over Division Rings

François Legrand, Elad Paran

Let $H$ be a division ring of finite dimension over its center, let $H [T]$ be the ring of polynomials in a central variable over $H$ , and let $H (T)$ be its quotient skew field. We…

math.CO2022

On Cayley graphs over generalized dicyclic groups

Angelot Behajaina, François Legrand

Recently, several works by a number of authors have studied integrality, distance integrality, and distance powers of Cayley graphs over some finite groups, such as dicyclic groups…

math.NT2022

On finite embedding problems with abelian kernels

François Legrand

Given a Hilbertian field $k$ and a finite set $S$ of Krull valuations of $k$ , we show that every finite split embedding problem $G \to Gal (L / k)$ over $k$ w…

math.NT2021

On parametric and generic polynomials with one parameter

Pierre Dèbes, Joachim König, François Legrand +1

Given fields $k \subseteq L$ , our results concern one parameter $L$ -parametric polynomials over $k$ , and their relation to generic polynomials. The former are polynomials $P(T,Y) \…

math.NT2020★ 1 cited

A note on finite embedding problems with nilpotent kernel

Arno Fehm, François Legrand

The first aim of this note is to fill a gap in the literature by proving that, given a global field $K$ and a finite set $S$ of primes of $K$ , every finite split embeddin…

math.NT2017

On the local behaviour of specializations of function field extensions

Joachim König, François Legrand, Danny Neftin

Given a field $k$ of characteristic zero and an indeterminate $T$ over $k$ , we investigate the local behaviour at primes of $k$ of finite Galois extensions of $k$ arising as specia…

math.NT2017

Automorphism groups over Hilbertian fields

François Legrand, Elad Paran

We show that every finite group occurs as the automorphism group of infinitely many finite (field) extensions of any given Hilbertian field. This extends and unifies previous resul…

math.NT2017

A note on prime divisors of polynomials $P (T^{k}), k \geq 1$

François Legrand

Let $F$ be a number field, $O_{F}$ the integral closure of $Z$ in $F$ and $P (T) \in O_{F} [T]$ a monic separable polynomial such that $P (0) \neq = 0$ and $P (1) \neq = 0$ . We give p…

math.NT2011

Twisted covers and specializations

Pierre Dèbes, François Legrand

The central topic is this question: is a given $k$ -étale algebra $\prod_{l} E_{l} / k$ the specialization of a given $k$ -cover $f : X \to B$ at some point $t_{0} \in B (k)$ ? Our main too…

math.NT2011

Specialization results in Galois theory

Pierre Dèbes, François Legrand

The paper has three main applications. The first one is this Hilbert-Grunwald statement. If $f:X\rightarrow \Pp^1$ is a degree $n$ $\Qq$-cover with monodromy group $S_{n}$ over $\bar…

Lüroth's and Igusa's theorems over Division Rings

On Cayley graphs over generalized dicyclic groups

On finite embedding problems with abelian kernels

On parametric and generic polynomials with one parameter

A note on finite embedding problems with nilpotent kernel

On the local behaviour of specializations of function field extensions

Automorphism groups over Hilbertian fields

A note on prime divisors of polynomials P(Tk),k≥1

Twisted covers and specializations

Specialization results in Galois theory

A note on prime divisors of polynomials $P (T^{k}), k \geq 1$