The Fargues-Scholze Correspondence over the Semisimple Generic Locus

Abstract: The moduli of semisimple generic L-parameters, introduced by Hansen, is a dense open substack of the moduli stack of L-parameters, and it is expected to be the largest open substack for which Fargues-Scholze’s categorical local Langlands correspondence can be understood reasonably explicitly. In this talk we show that much of the correspondence over this locus can indeed be made explicit, assuming certain properties of the correspondence such as geometric Eisenstein compatibility (currently known for GL(2)).

number theory

Audience: researchers in the topic

Comments: pre-talk at 3pm

UCSD number theory seminar

Series comments: Most talks are preceded by a pre-talk for graduate students and postdocs. The pre-talks start 40 minutes prior to the posted time (usually at 3:20pm Pacific) and last about 30 minutes.