Remarks on the arithmetic fundamental lemma

Li, Chao; Zhu, Yihang

doi:10.2140/ant.2017.11.2425

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Remarks on the arithmetic fundamental lemma

Chao Li and Yihang Zhu

Vol. 11 (2017), No. 10, 2425–2445

DOI: 10.2140/ant.2017.11.2425

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

Vol. 11, No. 10, 2017