  In this work we construct an eigencurve for p-adic modular forms attached to
an indefinite quaternion algebra over Q. Our theory includes the definition,
both as rules on test objects and sections of line bundle, of p-adic modular
forms, convergent and overconvergent, of any p-adic weight. We prove that our
modular forms can be put in analytic families over the weight space and we
introduce the Hecke operators U and T_l, that can also be put in families. We
show that the U-operator acts compactly on the space of overconvergent modular
forms. We finally construct the eigencurve, a rigid analytic variety whose
points correspond to systems of overconvergent eigenforms of finite slope with
respect to the U-operator.
