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On the arithmetic fundamental lemma in the minuscule case

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

Published online by Cambridge University Press:  04 July 2013

Michael Rapoport ,
Ulrich Terstiege  and
Wei Zhang
Michael Rapoport
Affiliation:
Mathematisches Institut der Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany email rapoport@math.uni-bonn.de
Ulrich Terstiege
Affiliation:
Institut für Experimentelle Mathematik, Universität Duisburg-Essen, Campus Essen, Ellernstraße 29, 45326 Essen, Germany email ulrich.terstiege@uni-due.de
Wei Zhang
Affiliation:
Department of Mathematics, Columbia University, New York, NY 10027, USA email wzhang@math.columbia.edu
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Abstract

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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 $p$-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.

Keywords

arithmetic Gan–Gross–Prasad conjecturearithmetic fundamental lemmaRapoport–Zink spacesspecial cycles

MSC classification

Secondary: 11G18: Arithmetic aspects of modular and Shimura varieties 14G17: Positive characteristic ground fields 22E55: Representations of Lie and linear algebraic groups over global fields and adèle rings
Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 10 , October 2013 , pp. 1631 - 1666
Copyright
© The Author(s) 2013 

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