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Arithmetic intersection on GSpin Rapoport–Zink spaces

Part of: Arithmetic problems. Diophantine geometry Lie groups Arithmetic algebraic geometry

Published online by Cambridge University Press:  16 May 2018

Chao Li  and
Yihang Zhu
Chao Li
Affiliation:
Department of Mathematics, Columbia University, 2990 Broadway, New York, NY 10027, USA email chaoli@math.columbia.edu
Yihang Zhu
Affiliation:
Department of Mathematics, Columbia University, 2990 Broadway, New York, NY 10027, USA email yihang@math.columbia.edu
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Abstract

We prove an explicit formula for the arithmetic intersection number of diagonal cycles on GSpin Rapoport–Zink spaces in the minuscule case. This is a local problem arising from the arithmetic Gan–Gross–Prasad conjecture for orthogonal Shimura varieties. Our formula can be viewed as an orthogonal counterpart of the arithmetic–geometric side of the arithmetic fundamental lemma proved by Rapoport–Terstiege–Zhang in the minuscule case.

Keywords

arithmetic Gan–Gross–Prasad conjectureRapoport–Zink spacesspinor groupsspecial cycles

MSC classification

Primary: 11G18: Arithmetic aspects of modular and Shimura varieties 14G17: Positive characteristic ground fields
Secondary: 22E55: Representations of Lie and linear algebraic groups over global fields and adèle rings

Information

Type
Research Article
Information
Compositio Mathematica , Volume 154 , Issue 7 , July 2018 , pp. 1407 - 1440
Copyright
© The Authors 2018 

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