Real multiplication curves by subfields of cyclotomic fields

Research paper by Ivan Boyer

Indexed on: 09 Oct '13Published on: 09 Oct '13Published in: Mathematics - Algebraic Geometry


In \emph{Endomorphism Algebras of Jacobians}, Ellenberg gives group theory tools to construct jacobians of curves with real multiplication. He shows the existence of curves and family of curves with real multiplication by subfields of cyclotomic fields. Among them, some are already known such as the family of Mestre, or the family of Tautz, Top and Verberkmoes. In this article, we give explicit families of real multiplication curves, for each case Ellenberg showed their existence.