1 citations · 1 across the 9 of their papers we have counts for
10 papers
Tschirnhausen bundles of sextic covers of
Sam Frengley, Sameera Vemulapalli
A degree genus cover of the complex projective line by a smooth irreducible curve yields a vector bundle on the projective line by pushforward of the structure sheaf. W…
Modular abelian surfaces of small conductor with nontrivial Tate--Shafarevich groups
Sam Frengley, Dylan Laird
We exhibit examples of geometrically simple abelian surfaces with conductor bounded by whose Tate--Shafarevich groups contain a subgroup isomorphic to…
Tschirnhausen Bundles of Quintic Covers of
Sam Frengley, Sameera Vemulapalli
A degree genus cover of the complex projective line by a smooth irreducible curve yields a vector bundle on the projective line by pushforward of the structure sheaf. W…
Galois groups of simple abelian varieties over finite fields and exceptional Tate classes
Santiago Arango-Piñeros, Sam Frengley, Sameera Vemulapalli
We prove new cases of the Tate conjecture for abelian varieties over finite fields, extending previous results of Dupuy--Kedlaya--Zureick-Brown, Lenstra--Zarhin, Tankeev, and Zarhi…
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…
On the geometry of the Humbert surface of square discriminant
Sam Frengley
For every positive integer we determine the Enriques--Kodaira type of the Humbert surface of discriminant which parametrises principally polarised abelian surfaces that a…
Explicit -torsion in the Tate-Shafarevich groups of genus Jacobians
Sam Frengley
Let be a genus curve whose Jacobian has real multiplication by a quadratic order in which splits. We describe an algorithm which outputs twist…
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 are known for . We obtain generic models for genus 2 curves over with real mu…
On -congruences of elliptic curves
Sam Frengley
We construct infinite families of pairs of (geometrically non-isogenous) elliptic curves defined over with -torsion subgroups that are isomorphic as Galois modules…
Congruences of elliptic curves arising from non-surjective mod Galois representations
Sam Frengley
We study -congruences between quadratic twists of elliptic curves. If has exactly two distinct prime factors we show that these are parametrised by double covers of certain…