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1 results

  • p-adic modular forms of non-integral weight over Shimura curves

  • Part of
  • Riccardo Brasca
  • Journal:
    Compositio Mathematica / Volume 149 / Issue 1 / January 2013
    Published online by Cambridge University Press:
    01 November 2012, pp. 32-62
    Print publication:
    January 2013

  • In this work, we set up a theory of p-adic modular forms over Shimura curves over totally real fields which allows us to consider also non-integral weights. In particular, we define an analogue of the sheaves of kth invariant differentials over the Shimura curves we are interested in, for any p-adic character. In this way, we are able to introduce the notion of overconvergent modular form of any p-adic weight. Moreover, our sheaves can be put in p-adic families over a suitable rigid analytic space, that parametrizes the weights. Finally, we define Hecke operators, including the U operator, that acts compactly on the space of overconvergent modular forms. We also construct the eigencurve.