Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-10T17:00:29.071Z Has data issue: false hasContentIssue false
  • English
  • Français

$\mathcal P$-adic modular forms over Shimura curves over totally real fields

Published online by Cambridge University Press:  04 December 2007

Payman L Kassaei
Payman L Kassaei
Affiliation:
Department of Mathematics, Brandeis University, MS 050, P.O. Box 9110, Waltham, MA 02454-9110, U.S.A.payman@brandeis.edu Department of Mathematics, McGill University, Montreal, Quebec H3A 2K6, Canada (e-mail: kassaei@math.mcgill.ca)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We set up the basic theory of $\mathcal P$-adic modular forms over certain unitary PEL Shimura curves M′K′. For any PEL abelian scheme classified by M′K′, which is not ‘too supersingular’, we construct a canonical subgroup which is essentially a lifting of the kernel of Frobenius from characteristic p. Using this construction we define the U and Frob operators in this context. Following Coleman, we study the spectral theory of the action of U on families of overconvergent $\mathcal P$-adic modular forms and prove that the dimension of overconvergent eigenforms of U of a given slope is a locally constant function of the weight.

Keywords

p-adic modular formsquaternionic and Hilbert modular formsShimura curvesthe U-operator11F85 (primary)11F5511F3314G35 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 2 , March 2004 , pp. 359 - 395
Copyright
Foundation Compositio Mathematica 2004