Michael Cerchia

activity

20192025

collaborators

4 papers

math.NT2025

Modular curves of prime-power level with infinitely many quadratic points

Michael Cerchia, Rakvi

We completely determine the $1085$ open subgroups $H$ of $GL_{2} (Z)$ of prime-power level that satisfy $- I \in H$ and $\operatorname{det}(H)=\wideha…

math.NT2025

Weil polynomials of abelian varieties over finite fields

Michael Cerchia, Zeyu Liu, Diana Mocanu +2

In this paper, we investigate Weil polynomials and their relationship with isogeny classes of abelian varieties over finite fields. We give a necessary condition for a degree 12 po…

math.NT2023

Section Rings of $Q$ -Divisors on Genus $1$ Curves

Michael Cerchia, Jesse Franklin, Evan O'Dorney

We compute generators and relations for the section ring of a rational divisor on an elliptic curve. Our technique generalizes the work of O'Dorney (in genus zero) and Voight--Zure…

math.NT2019

Uniform bounds on the image of the arboreal Galois representations attached to non-CM elliptic curves

Michael Cerchia, Jeremy Rouse

Let $ℓ$ be a prime number and let $F$ be a number field and $E / F$ a non-CM elliptic curve with a point $α \in E (F)$ of infinite order. Attached to the pair $(E, α)$ is the $ℓ$ -…

Modular curves of prime-power level with infinitely many quadratic points

Weil polynomials of abelian varieties over finite fields

Section Rings of Q-Divisors on Genus 1 Curves

Uniform bounds on the image of the arboreal Galois representations attached to non-CM elliptic curves

Section Rings of $Q$ -Divisors on Genus $1$ Curves