AI 中文总结
该研究为奇素数p下具极大parahoric水平的Shimura簇构造了可能的半稳定积分模型，利用局部模型图得到正则且具正规交叉特殊纤维的模型，还推导出惯性群相关作用的幂幺性。
AI 中文摘要
我们在奇素数p下，为一类具有极大 parahoric 水平的Shimura簇构造了（可能的）半稳定积分模型。主要输入是对相关典范局部模型的半稳定等变修改的显式构造，其中基础群是非分歧酉相似群、辛相似群或偶正交相似群的Weil限制。通过局部模型图，这些构造给出了对应Shimura簇的（可能的）半稳定积分模型。特别地，所得模型是正则的，且具有约化的特殊纤维，其为正规交叉型。作为应用，我们推导出惯性群对附近循环以及几何一般纤维的ℓ进上同调的作用是幂幺的。
英文摘要
We construct (potentially) semi-stable integral models for a class of Shimura varieties with maximal parahoric level at an odd prime $p$. The main input is an explicit construction of semi-stable equivariant modifications of the relevant canonical local models, where the underlying groups are Weil restrictions of unramified unitary similitude groups, symplectic similitude groups, or even orthogonal similitude groups. Via the local model diagram, these constructions give (potentially) semi-stable integral models of the corresponding Shimura varieties. In particular, the resulting models are regular and have reduced special fiber with normal crossings. As an application, we deduce the unipotence of the inertia action on nearby cycles and the $\ell$-adic cohomology of the geometric generic fibers.
Comments51 pp, comments welcome
