B. Poonen

collaborators

4 papers

math.NT2026

The Mathieu group $M_{23}$ is a Galois group over $Q$

Xiaoyu Huang, Blake Jackson, Kyu-Hwan Lee +3

Researchers studying the inverse Galois problem realized 25 of the 26 sporadic finite simple groups as Galois groups over $Q$ during 1984--1989. We complete this program b…

math.AG2025

The valuation of the discriminant of a hypersurface

Bjorn Poonen, Michael Stoll

Let $R$ be a discrete valuation ring, with valuation $v : R ↠ Z_{\geq 0} \cup {\infty}$ and residue field $k$ . Let $H$ be a hypersurface $\operatorn…

math.AG2025

Lattices in Tate modules

Bjorn Poonen, Sergey Rybakov

Refining a theorem of Zarhin, we prove that given a $g$ -dimensional abelian variety $X$ and an endomorphism $u$ of $X$ , there exists a matrix $A \in \operatorname{M}_{2g}(\mathbb{Z…

math.NT2025

Statistics of $K$ -groups modulo $p$ for the ring of integers of a varying quadratic number field

Bruce W. Jordan, Zev Klagsbrun, Bjorn Poonen +2

For each odd prime $p$ , we conjecture the distribution of the $p$ -torsion subgroup of $K_{2 n} (O_{F})$ as $F$ ranges over real quadratic fields, or over imaginary quadratic…

The Mathieu group M23​ is a Galois group over Q

The valuation of the discriminant of a hypersurface

Lattices in Tate modules

Statistics of K-groups modulo p for the ring of integers of a varying quadratic number field

The Mathieu group $M_{23}$ is a Galois group over $Q$

Statistics of $K$ -groups modulo $p$ for the ring of integers of a varying quadratic number field