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Galois $overline{mathbb F}_l$-monodromy, level fixing and Iharas lemma

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 Added by Pascal Boyer
 Publication date 2019
  fields
and research's language is English
 Authors Pascal Boyer




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We exhibit cases of a level fixing phenomenon for galoisian automorphic representations of a CM field $F$, with dimension $d geq 2$. The proof rests on the freeness of the localized cohomology groups of KHT Shimura varieties and the strictness of its filtration induced by the spectral sequence associated to the filtration of stratification of the nearby cycles perverse sheaf at some fixed place $v$ of $F$. The main point is the observation that the action of the unipotent monodromy operator at $v$ is then given by those on the nearby cycles where its order of nilpotency modulo $l$ equals those in characteristic zero. Finally we infer some consequences concerning level raising and Iharas lemma.



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59 - Pascal Boyer 2015
A key ingredient in the Taylor-Wiles proof of Fermat last theorem is the classical Iharas 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 Iharas lemma in higher dimension for some similitude groups. The main aim of this paper is then to prove some new instances of this generalized Iharas lemma by considering some particular non pseudo Eisenstein maximal ideals of unramified Hecke algebras. As a consequence, we prove a level rising statement.
49 - Pascal Boyer 2018
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163 - Pascal Boyer 2015
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