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THE -MODULAR LOCAL LANGLANDS CORRESPONDENCE AND LOCAL CONSTANTS
Journal of the Institute of Mathematics of Jussieu ( IF 1.1 ) Pub Date : 2019-11-08 , DOI: 10.1017/s1474748019000586 R. Kurinczuk , N. Matringe
Journal of the Institute of Mathematics of Jussieu ( IF 1.1 ) Pub Date : 2019-11-08 , DOI: 10.1017/s1474748019000586 R. Kurinczuk , N. Matringe
Let $F$ be a non-archimedean local field of residual characteristic $p$ , $\ell \neq p$ be a prime number, and $\text{W}_{F}$ the Weil group of $F$ . We classify equivalence classes of $\text{W}_{F}$ -semisimple Deligne $\ell$ -modular representations of $\text{W}_{F}$ in terms of irreducible $\ell$ -modular representations of $\text{W}_{F}$ , and extend constructions of Artin–Deligne local constants to this setting. Finally, we define a variant of the $\ell$ -modular local Langlands correspondence which satisfies a preservation of local constants statement for pairs of generic representations.
中文翻译:
- 模块化局部 LANGLANDS 对应和局部常数
让$F$ 是残差特征的非阿基米德局部场$p$ ,$\ell \neq p$ 是一个素数,并且$\文本{W}_{F}$ 韦尔集团$F$ . 我们对等价类进行分类$\文本{W}_{F}$ - 半简单的 Deligne$\ell$ -模块化表示$\文本{W}_{F}$ 就不可约而言$\ell$ -模块化表示$\文本{W}_{F}$ , 并将 Artin-Deligne 局部常数的构造扩展到此设置。最后,我们定义了一个变体$\ell$ -模块化局部朗兰兹对应,满足通用表示对的局部常数声明的保留。
更新日期:2019-11-08
中文翻译:
- 模块化局部 LANGLANDS 对应和局部常数
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