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IHARA LEMMA AND LEVEL RAISING IN HIGHER DIMENSION
Journal of the Institute of Mathematics of Jussieu ( IF 1.1 ) Pub Date : 2021-01-25 , DOI: 10.1017/s1474748020000729
Pascal Boyer

A key ingredient in the Taylor–Wiles proof of Fermat’s last theorem is the classical Ihara lemma, which is used to raise the modularity property between some congruent Galois representations. In their work on Sato and Tate, Clozel, Harris and Taylor proposed a generalisation of the Ihara lemma in higher dimension for some similitude groups. The main aim of this paper is to prove some new instances of this generalised Ihara lemma by considering some particular non-pseudo-Eisenstein maximal ideals of unramified Hecke algebras. As a consequence, we prove a level-raising statement.



中文翻译:

IHARA引理和更高维度的水平提升

费马大定理的 Taylor-Wiles 证明中的一个关键要素是经典的 Ihara 引理,它用于提高一些全等 Galois 表示之间的模块化属性。在他们关于 Sato 和 Tate 的工作中,Clozel、Harris 和 Taylor 提出了 Ihara 引理在更高维度上对一些相似群的推广。本文的主要目的是通过考虑非分支 Hecke 代数的一些特定的非伪 Eisenstein 极大理想来证明这个广义 Ihara 引理的一些新实例。因此,我们证明了一个水平提升声明。

更新日期:2021-01-25
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