Hida theory over some unitary Shimura varieties without ordinary locus

We develop Hida theory for Shimura varieties of type~A without ordinary locus. In particular we show that the dimension of the space of ordinary forms is bounded independently of the weight and that there is a module of $\Lambda$-adic cuspidal ordinary forms which is of finite type over $\Lambda$, w...

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Bibliographic Details
Published in:American journal of mathematics 2021-06, Vol.143 (3), p.715-751
Main Authors: Brasca, Riccardo, Rosso, Giovanni
Format: Article
Language:English
Subjects:
Loci
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Summary:We develop Hida theory for Shimura varieties of type~A without ordinary locus. In particular we show that the dimension of the space of ordinary forms is bounded independently of the weight and that there is a module of $\Lambda$-adic cuspidal ordinary forms which is of finite type over $\Lambda$, where $\Lambda$ is a twisted Iwasawa algebra.
ISSN:0002-9327
1080-6377
1080-6377
DOI:10.1353/ajm.2021.0017