In their study of local models of Shimura varieties for totally ramified extensions, Pappas and Rapoport posed a conjecture about the reducedness of a certain subscheme of n × n {n\times n} matrices. We give a positive answer to their conjecture in full generality. Our main ideas follow naturally from two of our previous works. The first is our proof of a conjecture of Kreiman, Lakshmibai, Magyar, and Weyman on the equations defining type A affine Grassmannians. The second is the work of the first two authors and Kamnitzer on affine Grassmannian slices and their reduced scheme structure. We also present a version of our argument that is almost completely elementary: the only non-elementary ingredient is the Frobenius splitting of Schubert varieties.

中文翻译：

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关于帕帕斯和拉坡波特关于GL_ d的标准局部模型的猜想

在对Shimura品种的局部扩展完全扩展的局部模型的研究中，Pappas和Rapoport提出了关于n×n {n \ times n}个矩阵的某些子类别的缩减性的一个猜想。我们完全笼统地对他们的猜想给出了肯定的答案。我们的主要思想自然而然地来自我们之前的两篇作品。首先是我们对Kreiman，Lakshmibai，Magyar和Weyman的猜想在定义A型仿射Grassmannian的方程式上的证明。第二个是前两个作者和Kamnitzer在仿射Grassmannian切片上的工作及其简化的方案结构。我们还提出了几乎完全基本的论点版本：唯一的非基本成分是舒伯特品种的Frobenius分裂。