Kudla–Rapoport arithmetic intersection conjecture for special cycles

Let $x_1,\dots,x_n\in {\mathbb V}$, where ${\mathbb V}$ is the hermitian space of special homomorphisms, and let $h$ be its hermitian form. Put

$$B=(h(x_i,x_j))_{1\leq i,j\leq n}.$$

The special cycles ${\mathcal Z}(x_1),\dots,{\mathcal Z}(x_n)$ are intersected in the unitary Rapoport–Zink space ${\mathcal N}^0_{E/F}(1,n-1)$. Kudla–Rapoport conjecture. Their arithmetic intersection number is

$$\langle {\mathcal Z}(x_1),\dots,{\mathcal Z}(x_n)\rangle:=\chi(O_{{\mathcal Z}(x_1)}\otimes^{\mathbb L}\dots\otimes^{\mathbb L}O_{{\mathcal Z}(x_n)})=\frac{\alpha'(1_n,B)}{\alpha(1_n,1_n)}.$$

Here $\chi$ is the Euler–Poincaré characteristic, $\otimes^{\mathbb L}$ is the derived tensor product, $\alpha$ is the representation density, and $\alpha'$ is its derivative. The conjecture was proved by Li and Zhang, so it is solved.