On the Arithmetic Fundamental Lemma in the minuscule case
  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. 
Michael Rapoport, Ulrich Terstiege, Wei Zhang
math.NT math.AG math.RT