Now showing items 1-5 of 5

  • Automorphisms and reduction of Heegner points on Shimura curves at Cerednik-Drinfeld primes 

    Molina Blanco, Santiago; Rotger Cerdà, Víctor (2014)
    Article
    Open Access
    The aim of this short note is to show how the interplay of the action of the automorphism group of a Shimura curve on the special fiber of its Cerednik-Drinfeld’s integral model at a prime of bad reduction and its sets ...
  • Equations of hyperelliptic Shimura curves 

    Molina Blanco, Santiago (2012)
    Article
    Open Access
    We describe a method for computing equations of hyperelliptic Shimura curves attached to indefinite quaternion algebras over Q and Atkin–Lehner quotients of them. It exploits Cerednik–Drinfeld 's non-archimedean uniformization ...
  • Parametrization of Abelian K-surfaces with quaternionic multiplication 

    Guitart Morales, Xavier; Molina Blanco, Santiago (2009-12)
    Article
    Restricted access - publisher's policy
    We prove that the Abelian K-surfaces whose endomorphism algebra is a rational quaternion algebra are parametrized, up to isogeny, by the K-rational points of the quotient of certain Shimura curves by the group of their ...
  • Ribet Bimodules and the Specialization of Heegner points 

    Molina Blanco, Santiago (2012)
    Article
    Open Access
    For a given order R in an imaginary quadratic field K, we study the specialization of the set CM(R) of Heegner points on the Shimura curve X = X0(D,N) at primes p | DN. As we show, if p does not divide the conductor of R, ...
  • The kernel of Ribet’s isogeny for genus three Shimura curves 

    Molina Blanco, Santiago; González Rovira, Josep (2015)
    Article
    Open Access
    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 ...