MULTIPLICITY ONE AT FULL CONGRUENCE LEVEL
Résumé
Abstract Let F be a totally real field in which p is unramified. Let ¯r:GF→GL2(¯Fp) be a modular Galois representation that satisfies the Taylor–Wiles hypotheses and is tamely ramified and generic at a place v above p . Let m be the corresponding Hecke eigensystem. We describe the m -torsion in the modp cohomology of Shimura curves with full congruence level at v as a GL2(kv) -representation. In particular, it only depends on ¯r|IFv and its Jordan–Hölder factors appear with multiplicity one. The main ingredients are a description of the submodule structure for generic GL2(Fq) -projective envelopes and the multiplicity one results of Emerton, Gee and Savitt [Lattices in the cohomology of Shimura curves, Invent. Math. 200 (1) (2015), 1–96].