Mathieu Florence

activity

20102026

most citedThe valuation criterion for normal basis generators

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

collaborators

7 papers

math.AG2026

Rationality problem for norm one tori of tensor products of étale algebras and Hasse norm principle

Mathieu Florence, Akinari Hoshi, Aiichi Yamasaki

Let $k$ be a field. Let $A = \prod_{i = 1}^{r} K_{i}$ and $B = \prod_{j = 1}^{s} E_{j}$ be étale $k$ -algebras where $K_{i}$ and $E_{j}$ are finite separable field extensions of $k$ with $[K_{i} : k] = m_{i}$ …

math.AG2025

Lifting Galois representations via Galois cohomology

Mathieu Florence

This is a survey paper, on recent progress around lifting Galois representations. I focused on approaches that solely rely on Galois cohomology. Emphasis is laid on material I talk…

math.NT2024

Lifting Galois representations via Kummer flags

Andrea Conti, Cyril Demarche, Mathieu Florence

Let $Γ$ be either i) the absolute Galois group of a local field $F$ , or ii) the topological fundamental group of a closed connected orientable surface of genus $g$ . In case i), ass…

math.AG2024

Algebraic Groups with Torsors That Are Versal for All Affine Varieties

Uriya A. First, Mathieu Florence, Zev Rosengarten

Let $k$ be a field and let $G$ be an affine algebraic group over $k$ . Call a $G$ -torsor weakly versal for a class of $k$ -schemes $C$ if it specializes to every $G$ -torsor over…

math.AG2023

Realisation of linear algebraic groups as automorphism groups

Mathieu Florence

Let $G$ be a linear algebraic group, over a field $F$ . We show that $G$ is isomorphic to the automorphism group scheme of a smooth projective $F$ -variety, defined as the blow-up of…

math.AG2020

Smooth profinite groups, II: the Uplifting Pattern

Mathieu Florence

This text presents a scheme-theoretic enhancement of the theory of smooth profinite groups and cyclotomic pairs, introduced in the paper `Smooth profinite groups, I'. To do so, our…

math.NT2010★ 1 cited

The valuation criterion for normal basis generators

Bart de Smit, Mathieu Florence, Lara Thomas

If $L / K$ is a finite Galois extension of local fields, we say that the valuation criterion $V C (L / K)$ holds if there is an integer $d$ such that every element $x \in L$ with valuati…