M. Florence

activity

20092022

most citedLifting Theorems and Smooth Profinite Groups

8 citations · 16 across the 11 of their papers we have counts for

collaborators

16 papers

math.AG2022

On composition of torsors

Mathieu Florence, Diego Izquierdo, Giancarlo Lucchini Arteche

Let $K$ be a field, let $X$ be a connected smooth $K$ -scheme and let $G, H$ be two smooth connected $K$ -group schemes. Given $Y \to X$ a $G$ -torsor and $Z \to Y$ an $H$ -torsor, we s…

math.AG2021★ 1 cited

Realisation of abelian varieties as automorphism groups

Mathieu Florence

Let $A / F$ be an abelian variety over a field. Does there exist a smooth projective $F$ -variety $X$ , such that $A$ is isomorphic to the automorphism group scheme of $X / F$ ? We show t…

math.AG2020

Smooth profinite groups, III: the Smoothness Theorem

Charles De Clercq, Mathieu Florence

Let $p$ be a prime. In this article, we prove the Smoothness Theorem, which asserts that a $(1, 1)$ -cyclotomic pair is $(n, 1)$ -cyclotomic, for all $n \geq 1$ . In the particular case…

math.RA2020

Common Splitting Fields of Symbol Algebras

Adam Chapman, Mathieu Florence, Kelly McKinnie

We study the common splitting fields of symbol algebras of degree $p^{m}$ over fields $F$ of $char (F) = p$ . We first show that if any finite number of such algebras shar…

math.AG2020

Smooth profinite groups, I: geometrizing Kummer theory

Charles De Clercq, Mathieu Florence

In this series of three papers, we introduce and study cyclotomic pairs and smooth profinite groups. They are a geometric axiomatisation of Kummer theory for fields, with coefficie…

math.AG2019

Residues on Affine Grassmannians

Mathieu Florence, Philippe Gille

Given a linear group G over a field k, we define a notion of index and residue of an element g of G(k((t)). This provides an alternative proof of Gabber's theorem stating that G ha…