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Overconvergent modular sheaves and modular forms for GL 2/F

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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.

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Authors and Affiliations

  1. Dipartimento di Matematica “Federigo Enriques”, Università degli Studi di Milano, Via C. Saldini 50, Milano, 20133, Italia

    Fabrizio Andreatta

  2. Department of Mathematics and Statistics, Concordia University, 1455 de Maison-neuve West Blvd., Montreal, Quebec, Canada

    Adrian Iovita

  3. Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova, Padova, Italy

    Adrian Iovita

  4. Department of Mathematics and Statistics, Boston University, 111 Cummington Street, Boston, MA, 02215, USA

    Glenn Stevens

Authors
  1. Fabrizio Andreatta
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  2. Adrian Iovita
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  3. Glenn Stevens
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Correspondence to Fabrizio Andreatta.

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Andreatta, F., Iovita, A. & Stevens, G. Overconvergent modular sheaves and modular forms for GL 2/F . Isr. J. Math. 201, 299–359 (2014). https://doi.org/10.1007/s11856-014-1045-8

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  • DOI: https://doi.org/10.1007/s11856-014-1045-8

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