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