Arithmetic fundamental lemma for the spherical Hecke algebra (Q6593241)

In a relative trace formula approach to the arithmetic Gan-Gross-Prasad conjecture, the arithmetic fundamental lemma conjecture relates the special value of the derivative of an orbital integral to an arithmetic intersection number on a Rapoport-Zink formal moduli space of \(p\)-divisible groups attached to a unitary group.\N\NIn the present paper, the authors propose a variant of the arithmetic fundamental lemma conjecture for the spherical Hecke algebra. The new point is the appearance of the Hecke operator and the definition of such Hecke operators compared to the above arithmetic fundamental lemma conjecture. They prove this conjecture for the case \(\mathrm{U}(1) \times \mathrm{U}(2)\).