Pappas–Rapoport–Smithling topological flatness conjecture for naive local models

Let F/F0F/F_0 be a quadratic extension, let (V,ϕ)(V,\phi) be a symmetric space of dimension 2n+22n+2, and let I[0,n]I\subset [0,n] be non-empty. Let \RMI\naive\RM^\naive_I be the naive local model over \COF0\CO_{F_0}, whose generic fiber is the orthogonal Grassmannian of maximal totally isotropic (n+1)(n+1)-dimensional subspaces of VV. Pappas–Rapoport–Smithling's topological flatness conjecture. The naive local model \RMI\naive\RM^\naive_I is topologically flat. This means that its generic fiber is Zariski dense in \RMI\naive\RM^\naive_I; the supplied source does not specify whether the conjecture is resolved.

Sources & referencesView supporting material

Primary source

Jie Yang, Ioannis Zachos and Zhihao Zhao, “On p-adic integral moduli schemes and local models for PEL type D”, arXiv:2602.23813 (2026).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.