A proof of the Kudla-Rapoport conjecture for Kr\"amer models
Number Theory
2023-07-04 v2 Algebraic Geometry
Representation Theory
Abstract
We prove the Kudla--Rapoport conjecture for Kr\"amer models of unitary Rapoport--Zink spaces at ramified places. It is a precise identity between arithmetic intersection numbers of special cycles on Kr\"amer models and modified derived local densities of hermitian forms. As an application, we relax the local assumptions at ramified places in the arithmetic Siegel--Weil formula for unitary Shimura varieties, which is in particular applicable to unitary Shimura vartieties associated to unimodular hermitian lattices over imaginary quadratic fields.
Keywords
Cite
@article{arxiv.2208.07988,
title = {A proof of the Kudla-Rapoport conjecture for Kr\"amer models},
author = {Qiao He and Chao Li and Yousheng Shi and Tonghai Yang},
journal= {arXiv preprint arXiv:2208.07988},
year = {2023}
}
Comments
82pp, final version, to appear in Invent. Math