Mathieu Florence

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math.AG2026

Rationality problem for norm one tori of tensor products of Ã©tale 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 Ã©tale $k$ -algebras where $K_{i}$ and $E_{j}$ are finite separable field extensions of $k$ with $[K_{i} : k] = m_{i}$ …

math.AG2025

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.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.AG2025

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…