Martin Azon

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math.NT2025

Effective Darmon's program for the generalised Fermat equation

Martin Azon

We follow the ideas of Darmon's program for solving infinite families of generalised Fermat equations of signatures $(p, p, r)$ and $(r, r, p)$ , where, $r$ is a fixed prime and $p$ is…

math.NT2024

Conductor exponents for families of hyperelliptic curves

Martin Azon, Mar Curcó-Iranzo, Maleeha Khawaja +2

We compute the conductor exponents at odd places using the machinery of cluster pictures of curves for three infinite families of hyperelliptic curves. These are families of Frey h…

math.NT2024

Abelian surfaces over $F_{q} (t)$ with large Tate-Shafarevich groups

Martin Azon

We produce an explicit sequence $(S_{a})_{a \geq 1}$ of abelian surfaces over the rational function field $F_{q} (t)$ whose Tate-Shafarevich groups are finite and…

Effective Darmon's program for the generalised Fermat equation

Conductor exponents for families of hyperelliptic curves

Abelian surfaces over Fq​(t) with large Tate-Shafarevich groups

Abelian surfaces over $F_{q} (t)$ with large Tate-Shafarevich groups