English

The canonical subgroup: a "subgroup-free" approach

Number Theory 2007-05-23 v1 Algebraic Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.math/0502401,
  title  = {The canonical subgroup: a "subgroup-free" approach},
  author = {Eyal Z. Goren and Payman L Kassaei},
  journal= {arXiv preprint arXiv:math/0502401},
  year   = {2007}
}

Comments

16 pages, 1 figure

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