The kernel of Ribet’s isogeny for genus three Shimura curves

There are exactly nine reduced discriminants D of indefinite quaternion algebras over Q for which the Shimura curve XD attached to D has genus 3. We present equations for these nine curves. Moreover, for each D we determine a subgroup c(D) of cuspidal divisors of degree zero of the new part of the J...

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Bibliographic Details
Authors: Molina Blanco, Santiago|||0000-0001-9420-2807, González Rovira, Josep|||0000-0002-9850-1609
Format: article
Publication Date:2015
Country:España
Institution:Universitat Politècnica de Catalunya (UPC)
Repository:UPCommons. Portal del coneixement obert de la UPC
Language:English
OAI Identifier:oai:upcommons.upc.edu:2117/86355
Online Access:https://hdl.handle.net/2117/86355
Access Level:Open access
Keyword:Arithmetical algebraic geometry
Shimura varieties
Algebra
Curves, Elliptic
Àlgebra
Corbes modulars
Aritmètica
Varietats de Shimura
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
Description
Summary:There are exactly nine reduced discriminants D of indefinite quaternion algebras over Q for which the Shimura curve XD attached to D has genus 3. We present equations for these nine curves. Moreover, for each D we determine a subgroup c(D) of cuspidal divisors of degree zero of the new part of the Jacobian of the modular curve of level D such that the abelian variety quotient by c(D) is the jacobian of the curve XD.