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THE
$\ell$-MODULAR LOCAL LANGLANDS CORRESPONDENCE AND LOCAL CONSTANTS
- Part of
-
- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 20 / Issue 5 / September 2021
- Published online by Cambridge University Press:
- 08 November 2019, pp. 1585-1635
- Print publication:
- September 2021
-
- Article
- Export citation
-
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.
