Regular formal moduli spaces and arithmetic transfer conjectures
  We define various formal moduli spaces of p-divisible groups which are regular, and morphisms between them. We formulate arithmetic transfer conjectures, which are variants of the arithmetic fundamental lemma conjecture of the third author in the presence of ramification. These conjectures include the AT conjecture of our previous joint paper. We prove these conjectures in low-dimensional cases. 
Michael Rapoport, Brian Smithling, Wei Zhang
math.NT math.AG math.RT