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Hida theory over some unitary Shimura varieties without ordinary locus
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 143, Number 3, June 2021
- pp. 715-751
- 10.1353/ajm.2021.0017
- Article
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Abstract
abstract:
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.
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