Local Langlands correspondences in $$\ell $$ -adic coefficients

Pub Date : 2024-06-21 DOI:10.1007/s00229-024-01582-y
Naoki Imai
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Abstract

Let \(\ell \) be a prime number different from the residue characteristic of a non-archimedean local field F. We give formulations of \(\ell \)-adic local Langlands correspondences for connected reductive algebraic groups over F, which we conjecture to be independent of a choice of an isomorphism between the \(\ell \)-adic coefficient field and the complex number field.

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$$ell $$ -adic系数中的本地朗兰兹对应关系
让 \(ell\) 是一个与非archimedean局部域F的残差特征不同的素数。我们给出了F上连接的还原代数群的\(ell\)-adic局部朗兰兹对应关系的公式,我们猜想它与\(ell\)-adic系数域和复数域之间的同构选择无关。
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