Morningside Center of Mathematics

Chinese Academy of Sciences

中国科学院晨兴数学中心

Morningside Center of Mathematics

Chinese Academy of Sciences

Title: | Arithmetic fundamental lemma in the minuscule case |

Speaker: | Yihang Zhu (Harvard University) |

Time: | 2017-6-15, 11:00-12:00 |

Place: | 610 |

Abstract: | The arithmetic fundamental lemma (AFL), formulated by Wei Zhang, is a key local ingredient in the relative trace formula approach to the arithmetic Gan-Gross-Prasad conjecture, which generalizes the famous Gross-Zagier formula. The AFL compares intersection numbers on Rapoport-Zink spaces with derivatives of orbital integrals. We compute the Rapoport-Zink space side in the AFL, under a minuscule assumption. In the unitary case our work recovers the proof of Rapoport-Terstiege-Zhang of the AFL; in the orthogonal case our computation is new, suggesting that a relative trace formula approach should also be possible. This is joint work with Chao Li. |

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