On arithmetic fundamental lemmas

Wei Zhang Columbia university

Number Theory mathscidoc:1703.24013

Inventiones mathematicae, 188, (1), 197-252, 2012.4
Abstract We present a relative trace formula approach to the Gross–Zagier formula and its generalization to higher-dimensional unitary Shimura vari- eties. As a crucial ingredient, we formulate a conjectural arithmetic funda- mental 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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  title={On arithmetic fundamental lemmas},
  author={Wei Zhang},
  booktitle={Inventiones mathematicae},
Wei Zhang. On arithmetic fundamental lemmas. 2012. Vol. 188. In Inventiones mathematicae. pp.197-252. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170315100443470565713.
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