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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

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

$F$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
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