works on
abelian varieties 22-torsion fields 1arithmetic geometry 1class number bounds 1complex multiplication 1cyclic galois extensions 1cyclotomic fields 1endomorphism algebras 1galois representations 1hecke characters 1imaginary quadratic multiplication 1

From the 2 of 4 linked papers with an AI index.

collaborators

4 papers

math.NT2026

Abelian threefolds with imaginary multiplication

Francesc Fité, Pip Goodman

The paper investigates abelian threefolds over number fields that admit multiplication by an imaginary quadratic field, constructs a related elliptic curve with potential complex m…

math.NT2026

Endomorphism algebras of abelian varieties with large cyclic 2-torsion field over a given field

Pip Goodman

The paper investigates the endomorphism algebras of abelian varieties over a number field whose 2‑torsion field is a large cyclic extension, providing criteria for endomorphisms to…

math.NT2026

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…

math.NT2024

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…