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- W1996417646 abstract "Beyond the crucial role they play in the foundations of the theory of overconver- gent modular forms, canonical subgroups have found new applications to analytic continuation of overconvergent modular forms. For such applications, it is essential to understand various numerical aspects of the canonical subgroup, and in particular, the precise extent of its over- convergence. In this paper, we develop a theory of canonical subgroups for a general class of curves (including the unitary and quaternionic Shimura curves), using formal and rigid ge- ometry. In our approach, we use the common geometric features of these curves rather than their (possible) specific moduli-theoretic description; it allows us to reproduce, for the classical cases, the optimal radii of definition for the canonical subgroup, usually derived by employing the theory of formal groups." @default.
- W1996417646 created "2016-06-24" @default.
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- W1996417646 date "2006-01-01" @default.
- W1996417646 modified "2023-09-30" @default.
- W1996417646 title "The canonical subgroup: a subgroup-free approach" @default.
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- W1996417646 doi "https://doi.org/10.4171/cmh/66" @default.
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