Relative unitary RZ-spaces and the Arithmetic Fundamental Lemma

Abstract

We verify new cases of the Arithmetic Fundamental Lemma (AFL) of Wei Zhang. This relies on a recursive algorithm which allows, under certain conditions, to reduce the AFL identity in question to an AFL identity in lower dimension. The main ingredient for this reduction is a comparison isomorphism between different moduli problems of PEL-type for p-divisible groups. The construction of this comparison isomorphism is based on the theory of relative displays and frames, as developed by Tobias Ahsendorf, Eike Lau and Thomas Zink.

arXiv commentThe article is now formulated uniformly for strict formal ${\mathcal{O}}_K$-modules. In particular, Chapters 2 and 3 were merged. We also added Lemma 6.1 on the finiteness of the intersection product. Various typos were corrected and some editorial changes made