Work

The geometry and arithmetic of bielliptic Picard curves

Year: 2025

Type: article

Abstract: We study the geometry and arithmetic of the curves and their associated Prym abelian surfaces . We prove a Torelli‐type theorem in this context and give a geometric proof of the fact that has quaternionic multiplication by the quaternion order of discriminant 6. 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.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70347

Authors: Jef Laga, Ari Shnidman

Institutions: University of Cambridge, Hebrew University of Jerusalem

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funders: Hebrew University of Jerusalem, European Research Council