1 citations · 1 across the 6 of their papers we have counts for
9 papers
Lüroth's and Igusa's theorems over Division Rings
François Legrand, Elad Paran
Let be a division ring of finite dimension over its center, let be the ring of polynomials in a central variable over , and let be its quotient skew field. We…
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…
On finite embedding problems with abelian kernels
François Legrand
Given a Hilbertian field and a finite set of Krull valuations of , we show that every finite split embedding problem over w…
On parametric and generic polynomials with one parameter
Pierre Dèbes, Joachim König, François Legrand +1
Given fields , our results concern one parameter -parametric polynomials over , and their relation to generic polynomials. The former are polynomials $P(T,Y) \…
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 and a finite set of primes of , every finite split embeddin…
On the local behaviour of specializations of function field extensions
Joachim König, François Legrand, Danny Neftin
Given a field of characteristic zero and an indeterminate over , we investigate the local behaviour at primes of of finite Galois extensions of arising as specia…