Local Langlands correspondences in $\ell$-adic coefficients

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.

19 pages

References in corpus (2)

• Geometric realization of the local Langlands correspondence for representations of conductor three
• The Jacobson--Morozov morphism for Langlands parameters in the relative setting

Cited by in corpus (1)

• Non-semi-stable loci in Hecke stacks and Fargues' conjecture