Görtz's flatness conjecture for ramified symplectic local models
Görtz's flatness conjecture for ramified symplectic local models
Let be totally ramified, and let be a self-dual periodic -lattice chain. Let denote the corresponding naive local model.
Görtz's flatness conjecture. For any self-dual periodic -lattice chain , is flat over
Topological flatness is known in the stated setting, and the naive, vertexwise, and local models agree topologically. The conjecture concerns equality of the schemes themselves and remains open in the supplied source.
Sources & referencesView supporting material
Primary source
G. Pappas, M. Rapoport and B. Smithling, “Local models of Shimura varieties, I. Geometry and combinatorics”, arXiv:1011.5551 (2011).
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