Title:  Arithmetic fundamental lemma in the minuscule case

Speaker: Yihang Zhu (Harvard University)

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

Place: MCM 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.