Local Langlands functoriality for Yu's supercuspidals I: Kaletha's parametrization

RESUMO

This is the first of two papers dedicated to the explicit computation of the Fargues--Scholze correspondence. In this first part, we construct (inspired by, and extending, Kaletha's explicit Local Langlands Correspondence for non-singular supercuspidal representations) semisimple inertial L-parameters for all cuspidal representations arising from Yu's constructions, with arbitrary coefficients. We then establish a characterization of this correpondence in terms of certain functoriality properties. This characterization will be used in the sequel paper in order to compute the Fargues--Scholze correspondence after restriction to inertia.