Ihara's lemma and level rising in higher dimension
arXiv:1511.00144 · doi:10.1017/S1474748020000729
Abstract
A key ingredient in the Taylor-Wiles proof of Fermat last theorem is the classical Ihara's lemma which is used to rise the modularity property between some congruent galoisian representations. In their work on Sato-Tate, Clozel-Harris-Taylor proposed a generalization of the Ihara's lemma in higher dimension for some similitude groups. The main aim of this paper is then to prove some new instances of this generalized Ihara's lemma by considering some particular non pseudo Eisenstein maximal ideals of unramified Hecke algebras. As a consequence, we prove a level rising statement.
References in corpus (6)
- Théorie de Lubin-Tate non abélienne l-entière
- Un cas simple de correspondance de Jacquet-Langlands modulo l
- p-adic Hodge-theoretic properties of étale cohomology with mod p coefficients, and the cohomology of Shimura varieties
- Sur la torsion dans la cohomologie des variétés de Shimura de Kottwitz-Harris-Taylor
- Congruences automorphes et torsion dans la cohomologie d'un système local d'Harris-Taylor
- Mirabolic group, ramified Newton stratification and cohomology of Lubin-Tate spaces