A Characterization Of The Relation Between Two L-Modular Correspondences

Let F be a non archimedean local field of residual characteristic p and l a prime number different from p. Let V denote Vigneras' l-modular local Langlands correspondence [7], between irreducible l-modular representations of GL(n)(F) and n-dimensional l-modular Deligne representations of the Weil group W-F. In [4], enlarging the space of Galois parameters to Deligne representations with non necessarily nilpotent operators allowed us to propose a modification of the correspondence of Vigneras into a correspondence C, compatible with the formation of local constants in the generic case. In this note, following a remark of Alberto Minguez, we characterize the modification C circle V-1 by a short list of natural properties.