Data di Pubblicazione:
2012
Citazione:
P-ADIC MODULAR FORMS OF NON-INTEGRAL WEIGHT OVER SHIMURA CURVES / R. Brasca ; relatore: F. Andreatta ; coordinatore: M. Peloso. Universita' degli Studi di Milano, 2012 Mar 07. 24. ciclo, Anno Accademico 2011. [10.13130/brasca-riccardo_phd2012-03-07].
Abstract:
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 k-th 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. We focus on the U operator, showing that it is completely continuous on the space of overconvergent modular forms.
Tipologia IRIS:
Tesi di dottorato
Keywords:
$p$-adic modular forms ; quaternionic modular forms ; modular forms of non-integral weight
Elenco autori:
R. Brasca
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