We prove an explicit formula for the arithmetic intersection number of diagonal cycles on GSpin Rapoport-Zink spaces in the minuscule case. This is a local problem arising from the arithmetic Gan-Gross-Prasad conjecture for orthogonal Shimura varieties. Our formula can be viewed as an orthogonal counterpart of the arithmetic-geometric side of the arithmetic fundamental lemma proved by Rapoport-Terstiege-Zhang in the minuscule case.
On the Arithmetic Fundamental Lemma in the minuscule case
Fine Deligne-Lusztig varieties and Arithmetic Fundamental Lemmas
The stabilization of the Frobenius--Hecke traces on the intersection cohomology of orthogonal Shimura varieties
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