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

Content Provider	Scilit
Author	Brasca, Riccardo
Copyright Year	2012
Description	Journal: Compositio Mathematica 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.
Ending Page	62
Starting Page	32
ISSN	00221295
e-ISSN	15705846
DOI	10.1112/s0010437x12000449
Journal	Compositio Mathematica
Issue Number	1
Volume Number	149
Language	English
Publisher	Wiley-Blackwell
Publisher Date	2013-01-01
Access Restriction	Open
Subject Keyword	Journal: Compositio Mathematica Applied Mathematics
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory

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