Béranger Seguin

activity

20242026

collaborators

8 papers

math.NT2026

Lifts of unramified twists and local-global principles

Fabian Gundlach, BÃ©ranger Seguin

We prove that two-step nilpotent $p$ -extensions of rational global function fields of characteristic $p$ satisfy a quantitative local-global principle when they are counted accordi…

math.AG2026

On matrices commuting with their Frobenius

Fabian Gundlach, BÃ©ranger Seguin

The Frobenius of a matrix $M$ with coefficients in $F ˉ_{p}$ is the matrix $I ¨ (M)$ obtained by raising each coefficient to the $p$ -th power. We consider the question of c…

math.GN2025

Flimsy Spaces

Robin Khanfir, BÃ©ranger Seguin

We study $n$ -flimsy spaces, which are the topological spaces that remain connected when removing fewer than $n$ points but become disconnected when removing exactly $n$ points. We…

math.AT2025

Counting Components of Hurwitz Spaces

BÃ©ranger Seguin

For a finite group $G$ , we obtain asymptotics for the number of connected components of Hurwitz spaces of marked $G$ -covers (of both the affine and projective lines) whose monodrom…

math.AC2025

Symmetries of various sets of polynomials

Let $K$ be a field of characteristic $0$ , and let $k \geq 2$ be an integer. We prove that every $K$ -linear bijection $f : K [X] \to K [X]$ strongly preserving the set of $k$ -fre…

math.NT2025

Asymptotics of extensions of simple $Q$ -algebras

We answer various questions concerning the distribution of extensions of a given central simple algebra $K$ over a number field. Specifically, we give asymptotics for the count of…