Remarks on the arithmetic fundamental lemma
Number Theory
2018-03-16 v2 Algebraic Geometry
Abstract
W. Zhang's arithmetic fundamental lemma (AFL) is a conjectural identity between the derivative of an orbital integral on a symmetric space with an arithmetic intersection number on a unitary Rapoport-Zink space. In the minuscule case, Rapoport-Terstiege-Zhang have verified the AFL conjecture via explicit evaluation of both sides of the identity. We present a simpler way for evaluating the arithmetic intersection number, thereby providing a new proof of the AFL conjecture in the minuscule case.
Cite
@article{arxiv.1705.05167,
title = {Remarks on the arithmetic fundamental lemma},
author = {Chao Li and Yihang Zhu},
journal= {arXiv preprint arXiv:1705.05167},
year = {2018}
}
Comments
Minor revisons, to appear in Algebra Number Theory