Béranger Seguin

activity

20222026

most citedStudy of a division-like property

1 citations · 1 across the 10 of their papers we have counts for

collaborators

11 papers

math.NT2026

Twisted Artin-Schreier Theory I: $(C_{p} ⋊ C_{p - 1})$ -extensions of local function fields

Béranger Seguin

Over any field $K$ of characteristic $p$ , we parametrize the $(C_{p} ⋊ C_{p - 1})$ -extensions of $K$ using pairs of elements $(g, a) \in K \times K^{\times}$ , via a "twisted" variant…

math.NT2026

Lifts of unramified twists and local-global principles

Fabian Gundlach, Béranger 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.GN2025

Flimsy Spaces

Robin Khanfir, Béranger 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.AG2025

On matrices commuting with their Frobenius

Fabian Gundlach, Béranger Seguin

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

math.NT2025

Counting two-step nilpotent wildly ramified extensions of function fields

Fabian Gundlach, Béranger Seguin

We study the asymptotic distribution of wildly ramified extensions of function fields in characteristic $p > 2$ , focusing on (certain) $p$ -groups of nilpotency class at most $2$ . R…

math.AT2024

Counting Components of Hurwitz Spaces

Béranger 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.AC2024

Symmetries of various sets of polynomials

Béranger Seguin

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.NT2024

Asymptotics of extensions of simple $Q$ -algebras

Fabian Gundlach, Béranger Seguin

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…

math.NT2023

Fields of Definition of Components of Hurwitz Spaces

Béranger Seguin

For a fixed finite group $G$ , we study the fields of definition of geometrically irreducible components of Hurwitz moduli schemes of marked branched $G$ -covers of the projective li…

math.RA2022★ 1 cited

Study of a division-like property

Robin Khanfir, Béranger Seguin

We introduce a weak division-like property for noncommutative rings: a nontrivial ring is fadelian if for all nonzero $a, x$ there exist $b, c$ such that $x = ab + c a$ . We prove properti…

math.NT2022

The Geometry of Rings of Components of Hurwitz Spaces

Béranger Seguin

We consider a variant of the ring of components of Hurwitz spaces introduced by Ellenberg, Venkatesh and Westerland. By focusing on Hurwitz spaces classifying covers of the project…

Twisted Artin-Schreier Theory I: (Cp​⋊Cp−1​)-extensions of local function fields

Lifts of unramified twists and local-global principles

Flimsy Spaces

On matrices commuting with their Frobenius

Counting two-step nilpotent wildly ramified extensions of function fields

Counting Components of Hurwitz Spaces

Symmetries of various sets of polynomials

Asymptotics of extensions of simple Q-algebras

Fields of Definition of Components of Hurwitz Spaces

Study of a division-like property

The Geometry of Rings of Components of Hurwitz Spaces

Twisted Artin-Schreier Theory I: $(C_{p} ⋊ C_{p - 1})$ -extensions of local function fields

Asymptotics of extensions of simple $Q$ -algebras