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2017 Remarks on the arithmetic fundamental lemma
Chao Li, Yihang Zhu
Algebra Number Theory 11(10): 2425-2445 (2017). 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.

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Chao Li. Yihang Zhu. "Remarks on the arithmetic fundamental lemma." Algebra Number Theory 11 (10) 2425 - 2445, 2017. https://doi.org/10.2140/ant.2017.11.2425

Information

Received: 26 May 2017; Revised: 6 September 2017; Accepted: 5 October 2017; Published: 2017
First available in Project Euclid: 1 February 2018

zbMATH: 06825456
MathSciNet: MR3744362
Digital Object Identifier: 10.2140/ant.2017.11.2425

Subjects:
Primary: 11G18
Secondary: 14G17 , 22E55

Keywords: arithmetic fundamental lemmas , arithmetic Gan–Gross–Prasad conjectures , Rapoport–Zink spaces , special cycles

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.11 • No. 10 • 2017
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