nLab
Weil-Deligne representation

Context

Representation theory

Arithmetic

Contents

Definition

Let

Definition

(Weil-Deligne representation)
A Weil-Deligne representation is a pair (ρ 0,N)(\rho_{0},N) where

and

  • NN is a nilpotent monodromy operator

satisfying

ρ 0(σ)Nρ 0(σ) 1=σN \rho_{0}(\sigma)N\rho_{0}(\sigma)^{-1} \;=\; \left\Vert \sigma \right\Vert N

for all σW F\sigma\in W_{F}.

References