, Volume 188, Issue 1, pp 197-252
Date: 25 Aug 2011

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.

To my friend Lin Chen (1981–2009)