Abelian threefolds with imaginary multiplication
Abstract
Abstract Let be an abelian threefold defined over a number field with potential multiplication by an imaginary quadratic field . Under mild assumptions on , if has signature (2,1) and the multiplication by is defined over , we attach to an elliptic curve defined over with potential complex multiplication by , whose attached Galois representation is determined by the Hecke character associated to the determinant of the compatible system of ‐adic representations of . We deduce that if is an imaginary quadratic field, then it necessarily has class number .
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Advanced Mathematical Identities
Publication details
- Journal / source
- Journal of the London Mathematical Society
- Volume
- 114
- Issue
- 1
- Publication date
- 1 July 2026
- Language
- EN