1 citations · 2 across the 5 of their papers we have counts for
6 papers
Semistable abelian varieties over with bad reduction at 19 only: an overview of the Fontaine--Schoof strategy
Francesco Campagna, Pip Goodman
In this paper we provide an overview of a strategy pioneered by Fontaine and heavily refined by Schoof to classify abelian varieties with prescribed bad reduction. Throughout the o…
Abelian threefolds with imaginary multiplication
Francesc Fité, Pip Goodman
Let be an abelian threefold defined over a number field with potential multiplication by an imaginary quadratic field . Under mild assumptions on , if has signatu…
Endomorphism algebras of abelian varieties with large cyclic 2-torsion field over a given field
Pip Goodman
In this article we study the endomorphism algebras of abelian varieties defined over a given number field with large cyclic 2-torsion fields. A key step in doing so is to p…
Cubic and quartic points on modular curves using generalised symmetric Chabauty
Josha Box, Stevan Gajović, Pip Goodman
Answering a question of Zureick-Brown, we determine the cubic points on the modular curves for as well as the quartic points on . To…
Superelliptic curves with large Galois images
Pip Goodman
Let and be primes. In this paper we study the mod Galois representations attached to curves of the form where is monic and has coefficients bel…
Restrictions on endomorphism rings of jacobians and their minimal fields of definition
Pip Goodman
Zarhin has extensively studied restrictions placed on the endomorphism algebras of Jacobians for which the Galois group associated to their 2-torsion is insoluble and 'large' (…