AI 中文总结
本文为辛型和正交型 Shimura 簇在极大抛物水平构造正则整模型，通过爆破 Schubert 簇实现等变修改，证明了 Pappas 猜想。
AI 中文摘要
我们为一大类具有辛型和正交型的 Shimura 簇构造了正则整模型，这些模型在奇素数 $p$ 处具有极大抛物子群水平。这些模型定义在反射域的整数环上，其特殊纤维具有法向交叉，且不可约分量的重数为一或二。我们的构造利用了对相应的辛型和分裂偶正交相似群的正则局部模型进行显式等变修改，其中微小余特征标对应于极大迷向 Grassmann 簇。这些修改是通过在特殊纤维中连续爆破 Schubert 簇获得的。这证明了在上述情形下，极大抛物子群水平处 Pappas 的等变修改猜想。
英文摘要
We construct regular integral models for a class of Shimura varieties of symplectic and orthogonal type with maximal parahoric level at an odd prime $p$. These models are defined over the ring of integers of the reflex field and have special fiber with normal crossings and irreducible components of multiplicity one or two. Our construction uses explicit equivariant modifications of the corresponding canonical local models for symplectic and split even orthogonal similitude groups, with the minuscule cocharacters corresponding to maximal isotropic Grassmannians. These modifications are obtained by successively blowing up Schubert varieties in the special fiber. This proves the equivariant modification conjecture of Pappas at maximal parahoric level in the above cases.
