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Article Dans Une Revue Journal of the Institute of Mathematics of Jussieu Année : 2022

MULTIPLICITY ONE AT FULL CONGRUENCE LEVEL

Daniel Le
Benjamin Schraen

Résumé

Abstract Let F be a totally real field in which p is unramified. Let ¯r:GFGL2(¯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].

Dates et versions

hal-03861885 , version 1 (20-11-2022)

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Daniel Le, Stefano Morra, Benjamin Schraen. MULTIPLICITY ONE AT FULL CONGRUENCE LEVEL. Journal of the Institute of Mathematics of Jussieu, 2022, 21 (2), pp.637-658. ⟨10.1017/S1474748020000225⟩. ⟨hal-03861885⟩
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