English

Relative unitary RZ-spaces and the Arithmetic Fundamental Lemma

Algebraic Geometry 2019-07-24 v2

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