A proof of Kudla-Rapoport conjecture for Kramer models at ramified primes

Abstract

In this talk, I will first talk about the Kudla-Rapoport conjecture, which suggests a precise identity between arithmetic intersection numbers of special cycles on Rapoport-Zink space and derived local densities of hermitian forms. Then I will discuss how to modify the original conjecture over ramified primes and how to prove the modified conjecture. On the geometric side, we completely avoid explicit calculation of intersection number and the use of Tate’s conjecture. On the analytic side, the key input is a surprisingly simple formula for derived primitive local density. This talk is based on joint work with Chao Li, Yousheng Shi and Tonghai Yang.

Speaker

Qiao He is a sixth year graduate student in the Department of Mathematics at University of Wisconsin-Madison. His advisor is Professor Tonghai Yang. He is broadly interested in number theory and arithmetic geometry.

个人主页：

https://people.math.wisc.edu/~qhe36/