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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 [Wang24].