p-adic Modular Forms over Shimura Curves over

  title={p-adic Modular Forms over Shimura Curves over},
  author={Steven G. Kleiman},
In this thesis, we set up the basic theory of p-adic modular forms over Shimura curves over Q, parallel to the classical case over modular curves. We define and study the structure of the spaces of p-adic modular forms with respect to certain quaternion algebras over Q. We study the relation of these modular forms with classical quaternionic modular forms. We prove a canonical subgroup theorem for false elliptic curves. That enables us to define the Frobenius morphism of p-adic modular… CONTINUE READING

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