The Kudla-Rapoport conjecture predicts a precise identity between the arithmetic intersection number of special cycles on unitary Rapoport-Zink spaces and the derivative of local representation densities of hermitian forms. It is a key local ingredient to establish the arithmetic Siegel-Weil formula and the arithmetic Rallis inner product formula, relating the height of special cycles on Shimura varieties to the derivative of Siegel Eisenstein series and L-functions. We will motivate this conjecture, explain a proof and discuss global applications.
This is joint work with Wei Zhang.
This talk is related to this arXiv paper.
This video is part of the Institute for Advanced Study‘s Number theory seminar.
