Back to Search
Start Over
Local Ihara's lemma and applications
- Source :
- IMRN 2021
- Publication Year :
- 2018
-
Abstract
- Persistence 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 sub-representation of a non-degenerate irreducible representation is non-degenerate. This is not true anymore 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 persistence and related to the notion of essentially absolutely irreducible and generic representations in the work of Emerton-Helm, remains true for lattices given by the cohomology of Lubin-Tate spaces. As an global application, we give a new construction of automorphic congruences in the Ribet spirit.
- Subjects :
- Mathematics - Number Theory
Subjects
Details
- Database :
- arXiv
- Journal :
- IMRN 2021
- Publication Type :
- Report
- Accession number :
- edsarx.1810.06020
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1093/imrn/rnab298