Sam Frengley

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20212026

most citedGeneric models for genus 2 curves with real multiplication

1 citations · 1 across the 9 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.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

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