C. Keyes

collaborators

4 papers

math.NT2026

On $p$ -adic solubility of $A x^{ℓ} + B y^{m} + C z^{n} = 0$

Santiago Arango-Piñeros, Christopher Keyes, Andrew Kobin

We study $p$ -adic solubility of generalized Fermat equations $A x^{ℓ} + B y^{m} + C z^{n} = 0$ for positive integers $ℓ, m, n$ . For all but finitely many primes $p$ , the probability of…

math.NT2026

Effective Bertini theorems and zeros of $p$ -adic forms of degrees 7 and 11

Lea Beneish, Christopher Keyes

We establish an effective Bertini-type theorem for hypersurfaces $X_{f} : f = 0$ defined over a finite field $k$ for which $f$ has no linear factors over the algebraic closure $…

math.NT2025

The integral Hasse principle for stacky curves associated to a family of generalized Fermat equations

Juanita Duque-Rosero, Christopher Keyes, Andrew Kobin +3

We characterize the integral Hasse principle for an infinite family of spherical stacky curves with genus $g \in [2/3, 1)$ that are defined using generalized Fermat equations, extend…

math.NT2025

Fields generated by points on superelliptic curves

Lea Beneish, Christopher Keyes

We give an asymptotic lower bound on the number of field extensions generated by algebraic points on superelliptic curves over $Q$ with fixed degree $n$ and discriminant b…

On p-adic solubility of Axℓ+Bym+Czn=0

Effective Bertini theorems and zeros of p-adic forms of degrees 7 and 11

The integral Hasse principle for stacky curves associated to a family of generalized Fermat equations

Fields generated by points on superelliptic curves

On $p$ -adic solubility of $A x^{ℓ} + B y^{m} + C z^{n} = 0$

Effective Bertini theorems and zeros of $p$ -adic forms of degrees 7 and 11