A Kudla-Rapoport Formula for Exotic Smooth Models of Odd Dimension

Abstract

In this article, we prove a Kudla-Rapoport conjecture for $\mathcal{Y}$-cycles on exotic smooth unitary Rapoport-Zink spaces of odd arithmetic dimension, i.e. the arithmetic intersection numbers for $\mathcal{Y}$-cycles equals the derivatives of local representation density. We also compare $\mathcal{Z}$-cycles and $\mathcal{Y}$-cycles on these RZ spaces. The method is to relate both geometric and analytic sides to the even dimensional case and reduce the conjecture to the results in arXiv:2101.09485.