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Genus two curves with quaternionic multiplication and modular Jacobian

Autor
Gonzalez, J.; Guàrdia, J.
Tipus d'activitat
Article en revista
Revista
Mathematics of computation
Data de publicació
2009-01
Volum
78
Número
265
Pàgina inicial
575
Pàgina final
589
DOI
https://doi.org/10.1090/S0025-5718-08-02165-0 Obrir en finestra nova
Projecte finançador
Curvas modulares y de Shimura y superficies abelianas
Repositori
http://hdl.handle.net/2117/1958 Obrir en finestra nova
https://arxiv.org/pdf/0805.1302.pdf Obrir en finestra nova
URL
http://www.ams.org/journals/mcom/2009-78-265/S0025-5718-08-02165-0/S0025-5718-08-02165-0.pdf Obrir en finestra nova
Resum
We describe a method to determine all the isomorphism classes of principal polarizations of the modular abelian surfaces $A_f$ with quaternionic multiplication attached to a normalized newform $f$ without complex multiplication. We include an example of $A_f$ with quaternionic multiplication for which we find numerically a curve $C$ whose Jacobian is $A_f$ up to numerical approximation, and we prove that it has quaternionic multiplication and is isogenous to $A_f$. We describe a method to det...
Paraules clau
Genus two curves, Modular abelian surfaces, Quaternionic multiplication
Grup de recerca
TN - Grup de Recerca en Teoria de Nombres

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