Multiplicative Hitchin Fibrations and the Fundamental Lemma

A proof of the endoscopic fundamental lemma for spherical Hecke algebras using a new comprehensive framework of multiplicative Hitchin fibrations

This book develops a comprehensive framework of multiplicative Hitchin fibrations, which is a novel analogue of the classical Hitchin fibrations, and then uses it to prove the endoscopic fundamental lemma for spherical Hecke algebras over local function fields. Unlike previous proofs of similar results, it does not rely on r…