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Israel Journal of Mathematics

, Volume 201, Issue 1, pp 299–359 | Cite as

Overconvergent modular sheaves and modular forms for GL 2/F

  • Fabrizio AndreattaEmail author
  • Adrian Iovita
  • Glenn Stevens
Article

Abstract

Given a totally real field F and a prime integer p which is unramified in F, we construct p-adic families of overconvergent Hilbert modular forms (of non-necessarily parallel weight) as sections of, so called, overconvergent Hilbert modular sheaves. We prove that the classical Hilbert modular forms of integral weights are overconvergent in our sense. We compare our notion with Katz’s definition of p-adic Hilbert modular forms. For F = ℚ, we prove that our notion of (families of) overconvergent elliptic modular forms coincides with those of R. Coleman and V. Pilloni.

Keywords

Modular Form Galois Group Group Scheme Abelian Scheme Subgroup Scheme 
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Copyright information

© Hebrew University Magnes Press 2014

Authors and Affiliations

  • Fabrizio Andreatta
    • 1
    Email author
  • Adrian Iovita
    • 2
    • 3
  • Glenn Stevens
    • 4
  1. 1.Dipartimento di Matematica “Federigo Enriques”Università degli Studi di MilanoMilanoItalia
  2. 2.Department of Mathematics and StatisticsConcordia UniversityMontrealCanada
  3. 3.Dipartimento di Matematica Pura ed ApplicataUniversità degli Studi di PadovaPadovaItaly
  4. 4.Department of Mathematics and StatisticsBoston UniversityBostonUSA

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