Topological flatness of orthogonal local models in the split, even case. I

Details Topological flatness of orthogonal local models in the split, even case. I Topological flatness of orthogonal local models in the split, even case. I

2009-04-23

arxiv.org/abs/0904.3548v2

Mathematics

Algebraic Geometry

29 pages. Corrected description of the affine flag variety; references added; other minor revisions.

Scientific paper

Local models are schemes, defined in terms of linear algebra, that were introduced by Rapoport and Zink to study the \'etale-local structure of integral models of certain PEL Shimura varieties over p-adic fields. A basic requirement for the integral models, or equivalently for the local models, is that they be flat. In the case of local models for even orthogonal groups, Genestier observed that the original definition of the local model does not yield a flat scheme. In a recent article, Pappas and Rapoport introduced a new condition to the moduli problem defining the local model, the so-called spin condition, and conjectured that the resulting "spin" local model is flat. We prove a weak form of their conjecture in the split, Iwahori case, namely that the spin local model is topologically flat. An essential combinatorial ingredient is the equivalence of mu-admissibility and mu-permissibility for two minuscule cocharacters mu in root systems of type D.

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