Relative Fundamental Lemmas for Spherical Hecke Algebras and Multiplicative Hitchin Fibrations: the Jacquet--Rallis Case

We prove the Jacquet–Rallis fundamental lemma for spherical Hecke algebras over local function fields using multiplicative Hitchin fibrations. Our work is inspired by the proof of [Yun11] in the Lie algebra case and builds upon the general framework of multiplicative Hitchin fibrations in [Wang26].