C. Keyes

activity

20242026

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.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

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.NT2024

How often does a cubic hypersurface have a rational point?

Lea Beneish, Christopher Keyes

A cubic hypersurface in $P^{n}$ defined over $Q$ is given by the vanishing locus of a cubic form $f$ in $n + 1$ variables. It is conjectured that when $n \geq 4$ , suc…

On p-adic solubility of Axℓ+Bym+Czn=0

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

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

How often does a cubic hypersurface have a rational point?

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