The geometry and arithmetic of bielliptic Picard curves
Algebraic Geometry
2024-12-10 v3 Number Theory
Abstract
We study the geometry and arithmetic of the curves and their associated Prym abelian surfaces . We prove a Torelli theorem in this context and give a geometric proof of the fact that has quaternionic multiplication (QM) by the quaternion order of discriminant . This allows us to describe the Galois action on the geometric endomorphism algebra of . As an application, we classify the torsion subgroups of the Mordell-Weil groups , as both abelian groups and -modules.
Keywords
Cite
@article{arxiv.2308.15297,
title = {The geometry and arithmetic of bielliptic Picard curves},
author = {Jef Laga and Ari Shnidman},
journal= {arXiv preprint arXiv:2308.15297},
year = {2024}
}
Comments
37 pages, minor changes