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Local models are schemes, defined in terms of linear algebra, that wereintroduced by Rapoport and Zink to study the \'etale-local structure ofintegral models of certain PEL Shimura varieties over p-adic fields. A basicrequirement for the integral models, or equivalently for the local models, isthat they be flat. In the case of local models for even orthogonal groups,Genestier observed that the original definition of the local model does notyield a flat scheme. In a recent article, Pappas and Rapoport introduced a newcondition to the moduli problem defining the local model, the so-called spincondition, and conjectured that the resulting "spin" local model is flat. Weprove a weak form of their conjecture in the split, Iwahori case, namely thatthe spin local model is topologically flat. An essential combinatorialingredient is the equivalence of mu-admissibility and mu-permissibility for twominuscule cocharacters mu in root systems of type D.

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