On the Arithmetic Fundamental Lemma in the minuscule case

Abstract

The arithmetic fundamental lemma conjecture of the third author connects the derivative of an orbital integral on a symmetric space with an intersection number on a formal moduli space of $p$-divisible groups of Picard type. It arises in the relative trace formula approach to the arithmetic Gan-Gross-Prasad conjecture. We prove this conjecture in the minuscule case.

Referee's comments incorporated; in particular, the existence of frames for using the theory of displays in the proofs of Theorems 9.4 and 9.5 is clarified. To appear in Compositio Math

References in corpus (2)

• Multiplicity one Conjectures
• Intersections of special cycles on the Shimura variety for GU(1,2)

Cited by in corpus (22)

• On the arithmetic transfer conjecture for exotic smooth formal moduli spaces
• Basic loci in Shimura varieties of Coxeter type
• Fully Hodge-Newton decomposable Shimura varieties
• Arithmetic diagonal cycles on unitary Shimura varieties
• Fine Deligne-Lusztig varieties and Arithmetic Fundamental Lemmas
• Arithmetic intersection on GSpin Rapoport-Zink spaces
• La variante infinitésimale de la formule des traces de Jacquet-Rallis pour les groupes linéaires
• Weil representation and Arithmetic Fundamental Lemma
• Remarks on the arithmetic fundamental lemma
• The supersingular locus of the Shimura variety for GU(1,n-1) over a ramified prime
• Hecke and Galois Properties of Special Cycles on Unitary Shimura Varieties
• Local Constancy of Intersection Numbers
• On quaternionic unitary Rapoport-Zink spaces with parahoric level structures
• On supersingular loci of Shimura varieties for quaternionic unitary groups of degree $2$
• Regular formal moduli spaces and arithmetic transfer conjectures
• An arithmetic intersection conjecture
• Horizontal Distribution Relations for Special Cycles on Unitary Shimura Varieties: Split Case
• Deligne-Lusztig varieties and basic EKOR strata
• Fourier-Jacobi cycles and arithmetic relative trace formula (with an appendix by Chao Li and Yihang Zhu)
• The Gross-Zagier-Zhang formula over function fields
• On the regularity of special difference divisors
• An Arithmetic Transfer Identity