Hanson Smith

activity

20172026

most citedMonogenic fields arising from trinomials

12 citations · 13 across the 8 of their papers we have counts for

collaborators

13 papers

math.NT2026

Number Fields with Arbitrarily Large Minimal Index

Hanson Smith

For a number field $K / Q$ , the minimal index is the least positive integer $m$ for which there exists a monogenic order with index $m$ in the maximal order. For any $n > 2$ a…

math.NT2023

Radical Dynamical Monogenicity

Hanson Smith

Let $a$ be an integer and $p$ a prime so that $f (x) = x^{p} - a$ is irreducible. Write $f^{n} (x)$ to indicate the $n$ -fold composition of $f (x)$ with itself. We study the monogenicity of n…

math.AG2022

The Scheme of Monogenic Generators II: Local Monogenicity and Twists

Sarah Arpin, Sebastian Bozlee, Leo Herr +1

This is the sequel paper to arXiv:2108.07185, continuing a study of monogenicity of number rings from a moduli-theoretic perspective. By the results of the first paper in this seri…

math.NT2021

Frobenius Finds Non-monogenic Division Fields of Abelian Varieties

Hanson Smith

Let $A$ be an abelian variety over a finite field $k$ with $∣ k ∣ = q = p^{m}$ . Let $π \in End_{k} (A)$ denote the Frobenius and let $v = \frac{q}{π}$ denote Verschiebung. Suppose the Weil…

math.AG2021

The Scheme of Monogenic Generators I: Representability

Sarah Arpin, Sebastian Bozlee, Leo Herr +1

This is the first in a series of two papers that study monogenicity of number rings from a moduli-theoretic perspective. Given an extension of algebras $B / A$ , when is $B$ generated…

math.NT2020

Non-monogenic Division Fields of Elliptic Curves

Hanson Smith

For various positive integers $n$ , we show the existence of infinite families of elliptic curves over $Q$ with $n$ -division fields, $Q (E [n])$ , that are not monoge…