Michael Cerchia

collaborators

3 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.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 $ℓ$ -…