On the Arithmetic Fundamental Lemma in the minuscule case
Number Theory
2014-02-18 v3 Algebraic Geometry
Representation Theory
Abstract
The arithmetic fundamental lemma conjecture of the third author connects the derivative of an orbital integral on a symmetric space with an intersection number on a formal moduli space of -divisible groups of Picard type. It arises in the relative trace formula approach to the arithmetic Gan-Gross-Prasad conjecture. We prove this conjecture in the minuscule case.
Cite
@article{arxiv.1203.5827,
title = {On the Arithmetic Fundamental Lemma in the minuscule case},
author = {Michael Rapoport and Ulrich Terstiege and Wei Zhang},
journal= {arXiv preprint arXiv:1203.5827},
year = {2014}
}
Comments
Referee's comments incorporated; in particular, the existence of frames for using the theory of displays in the proofs of Theorems 9.4 and 9.5 is clarified. To appear in Compositio Math