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If is a modular form of weight , the representation of attached to it by the -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 -adique et changement de poids. J. Eur. Math. Soc. 21 (2018), no. 3, pp. 797–838