论文标题
当地模型的奇异性
Singularities of local models
论文作者
论文摘要
我们构建了Shimura品种的当地模型并调查其奇异性，并特别强调了大受欢迎的病例。更确切地说，除了残留特征中的奇数单一群体$ 2 $我们构建本地模型外，其特殊纤维，Cohen $ - $ MACAULAYNESS的降低，也表现出等级（伪）合理性的降低。在混合特征中，我们猜想了它们的（伪）合理性。这是基于对二维基础的帕哈里克群体方案的构建，用于使用完美的几何形状，以分析具有阳性特征的附属舒伯特品种的奇异性。
We construct local models of Shimura varieties and investigate their singularities, with special emphasis on wildly ramified cases. More precisely, with the exception of odd unitary groups in residue characteristic $2$ we construct local models, show reducedness of their special fiber, Cohen$-$Macaulayness and in equi-characteristic also (pseudo-)rationality. In mixed characteristic we conjecture their (pseudo-)rationality. This is based on the construction of parahoric group schemes over two-dimensional bases for wildly ramified groups and an analysis of singularities of the attached Schubert varieties in positive characteristic using perfect geometry.
