Vol. 11, No. 10, 2017

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Remarks on the arithmetic fundamental lemma

Chao Li and Yihang Zhu

Vol. 11 (2017), No. 10, 2425–2445
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 and 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.

Keywords
arithmetic Gan–Gross–Prasad conjectures, arithmetic fundamental lemmas, Rapoport–Zink spaces, special cycles
Mathematical Subject Classification 2010
Primary: 11G18
Secondary: 14G17, 22E55
Milestones
Received: 26 May 2017
Revised: 6 September 2017
Accepted: 5 October 2017
Published: 31 December 2017
Authors
Chao Li
Department of Mathematics
Columbia University
New York, NY
United States
Yihang Zhu
Department of Mathematics
Columbia University
New York, NY
United States