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On arithmetic fundamental lemmas

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Abstract

We present a relative trace formula approach to the Gross–Zagier formula and its generalization to higher-dimensional unitary Shimura varieties. As a crucial ingredient, we formulate a conjectural arithmetic fundamental lemma for unitary Rapoport–Zink spaces. We prove the conjecture when the Rapoport–Zink space is associated to a unitary group in two or three variables.

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Authors and Affiliations

  1. Department of Mathematics, Harvard University, One Oxford Street, Cambridge, MA, 02138, USA

    Wei Zhang

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  1. Wei Zhang
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Correspondence to Wei Zhang.

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To my friend Lin Chen (1981–2009)

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Zhang, W. On arithmetic fundamental lemmas. Invent. math. 188, 197–252 (2012). https://doi.org/10.1007/s00222-011-0348-1

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  • DOI: https://doi.org/10.1007/s00222-011-0348-1

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