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Article Dans Une Revue International Mathematics Research Notices Année : 2021

Local Ihara's lemma and applications

Résumé

Persitence of non degeneracy is a phenomenon which appears in the theory of $\overline{\mathbb{Q}}_l$-representations of the linear group: every irreducible submodule of the restriction to the mirabolic subgroup of an non degenerate irreducible representation is non degenerate. This is no more true in general, if we look at the modulo l reduction of some stable lattice. As in the Clozel-Harris-Taylor generalization of global Ihara's lemma, we show that this property, called non degeneracy persitence, remains true for lattices given by the cohomology of Lubin-Tate spaces.
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hal-01895168 , version 1 (14-10-2018)

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  • HAL Id : hal-01895168 , version 1

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Pascal Boyer. Local Ihara's lemma and applications. International Mathematics Research Notices, 2021, https://doi.org/10.1093/imrn/rnab298. ⟨hal-01895168⟩
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