正交局部模型在分裂偶情况下的拓扑平坦性。I
Topological flatness of orthogonal local models in the split, even case. I
摘要：
局部模型是Rapoport和Zink为了研究p-adic域上的某些PEL Shimura簇的积分模型的实-局部结构而引入的一种用线性代数定义的方案。对于积分模型或等效地对于局部模型的基本要求是它们是平坦的。在局部模型的情况下，甚至正交群，Genestier观察到，原来的定义的局部模型不产生一个平坦的计划。在最近的一篇文章中，Pappas和Rapoport为定义局部模型的模问题引入了一个新的条件，即所谓的自旋条件，并证明由此产生的“自旋”局部模型是平坦的。我们证明了他们的猜想在分裂，岩堀的情况下，即自旋局部模型是拓扑平坦的弱形式。D型根系中两个极小余特征标μ的μ容许性与μ容许性的等价性是一个重要的组合成分。
英文摘要：
Local models are schemes, defined in terms of linear algebra, that were introduced by Rapoport and Zink to study the étale-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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