JournalsjemsVol. 21, No. 3pp. 797–838

Correspondance de Langlands locale pp-adique et changement de poids

  • Pierre Colmez

    Université Pierre et Marie Curie, Paris, France
Correspondance de Langlands locale $p$-adique et changement de poids cover

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Abstract

If ff is a modular form of weight 1≥ 1, the representation of GL2(Qp)\mathbf {GL}_2(\mathbf Q_p) attached to it by the pp-adic local Langlands correspondence encodes the representation attached by the classical correspondence. We introduce weight shifting techniques that allow us to extend the result to weight 1. We also give a full description of the Jordan–Hölder components of the locally analytic representations appearing in the correspondence.

Cite this article

Pierre Colmez, Correspondance de Langlands locale pp-adique et changement de poids. J. Eur. Math. Soc. 21 (2018), no. 3, pp. 797–838

DOI 10.4171/JEMS/851