The canonical subgroup: a "subgroup-free" approach

Details The canonical subgroup: a "subgroup-free" approach The canonical subgroup: a "subgroup-free" approach

2005-02-18

arxiv.org/abs/math/0502401v1

Mathematics

Number Theory

16 pages, 1 figure

Scientific paper

Beyond the crucial role they play in the foundations of the theory of overconvergent 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 overconvergence. We develop a theory of canonical subgroups for a general class of curves (including the unitary and quaternionic Shimura curves), using formal and rigid geometry. In our approach, we use the common geometric features of these curves rather than their (possible) specific moduli-theoretic description.

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