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.
Keywords
Cite
@article{arxiv.1611.06520,
title = {Relative unitary RZ-spaces and the Arithmetic Fundamental Lemma},
author = {Andreas Mihatsch},
journal= {arXiv preprint arXiv:1611.06520},
year = {2019}
}
Comments
The 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