The Arithmetic Fundamental Lemma (AFL) arises from the Relative Trace Formula approach to the Gross–Zagier formula and generalizes the Guo–Jacquet Fundamental Lemma. In this talk, we review recent progress on the linear AFL and introduce our collaborative project on higher derivatives with Andreas Mihatsch and Wei Zhang. Our work explores the interpretation of higher derivatives of Guo–Jacquet orbital integrals through intersection numbers on local Shtukas. This result is a local field analogue of Yun and Zhang’s work on higher Gross–Zagier formula. We will introduce the geometrization of Guo–Jacquet Fundamental Lemma for the function field and describe its Hitchin fibration.