Local Langlands correspondences in $\ell$-adic coefficients

Naoki Imai

Local Langlands correspondences in $\ell$-adic coefficients

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arxiv 2003.14154 v4 pith:CLZVG2V4 submitted 2020-03-31 math.NT math.RT

Naoki Imai This is my paper · ORCID

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keywords adicfieldlocalcorrespondenceslanglandsnumberalgebraiccharacteristic

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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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