The modified Kudla–Rapoport conjecture for maximal parahoric Rapoport–Zink spaces

Let $L\subset \mathbb{V}$ be an $O_F$-lattice. The modified derived local density is

$$\partial\mathrm{Den}_{n,h}(L)=\mathrm{Den}_{n,h}'(L)+\sum_{i=0}^{\lfloor\frac{h-1}{2}\rfloor}c_{n,h-1-2i}\cdot\mathrm{Den}_{n,h-1-2i}(L),$$

where the coefficients $c_{n,i}\in\mathbb{Q}$ are chosen so that $\partial\mathrm{Den}_{n,h}(\Lambda_i)=0$ for vertex lattices $\Lambda_i$ of the indicated types. Here $\mathrm{Int}_{n,h}(L)$ denotes the arithmetic intersection number and $\partial\mathrm{Den}_{n,h}(L)$ the modified derived local density. Modified Kudla–Rapoport conjecture. For every such $L$,

$$\mathrm{Int}_{n,h}(L)=\partial\mathrm{Den}_{n,h}(L).$$

This is the proposed Kudla–Rapoport formula for the bad-reduction Rapoport–Zink space $\mathcal{N}_n^{[h]}$. The naive formula using $\mathrm{Den}_{n,h}'(L)$ fails for vertex lattices of type less than $h$, motivating the correction terms; the conjecture is presented without a resolution in the source.