Sam Frengley

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20242026

most citedGeneric models for genus 2 curves with real multiplication

1 citations · 1 across the 5 of their papers we have counts for

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math.NT2024

Galois groups of low dimensional abelian varieties over finite fields

Santiago Arango-Piñeros, Sam Frengley, Sameera Vemulapalli

We consider three isogeny invariants of abelian varieties over finite fields: the Galois group, Newton polygon, and the angle rank. Motivated by work of Dupuy, Kedlaya, and Zureick…

math.AG2024

On the geometry of the Humbert surface of square discriminant

Sam Frengley

For every positive integer $N$ we determine the Enriques--Kodaira type of the Humbert surface of discriminant $N^{2}$ which parametrises principally polarised abelian surfaces that a…

math.NT2024

Explicit $7$ -torsion in the Tate-Shafarevich groups of genus $2$ Jacobians

Sam Frengley

Let $C / Q$ be a genus $2$ curve whose Jacobian $J / Q$ has real multiplication by a quadratic order in which $7$ splits. We describe an algorithm which outputs twist…

math.NT2024★ 1 cited

Generic models for genus 2 curves with real multiplication

Alex Cowan, Sam Frengley, Kimball Martin

Explicit models of families of genus 2 curves with multiplication by $D$ are known for $D = 2, 3, 5$ . We obtain generic models for genus 2 curves over $Q$ with real mu…

Galois groups of low dimensional abelian varieties over finite fields

On the geometry of the Humbert surface of square discriminant

Explicit 7-torsion in the Tate-Shafarevich groups of genus 2 Jacobians

Generic models for genus 2 curves with real multiplication

Explicit $7$ -torsion in the Tate-Shafarevich groups of genus $2$ Jacobians