Relative unitary RZ-spaces and the Arithmetic Fundamental Lemma

TL;DR

This paper verifies new cases of the Arithmetic Fundamental Lemma using a recursive reduction approach based on comparison isomorphisms between moduli problems of PEL-type for p-divisible groups.

Contribution

It introduces a recursive algorithm for reducing AFL identities to lower dimensions and constructs a comparison isomorphism using the theory of relative displays and frames.

Findings

Verified new cases of the AFL

Developed a recursive reduction method

Constructed a comparison isomorphism

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.