This thesis is about integral models of Shimura varieties with emphasis on the reduction at the prime $p=2$.In the first part of the thesis, we construct local models for wildly ramified unitary similitude groups of odd dimension $n\geq 3$ with special parahoric level structure and signature $(n-1,1)$. We first give a lattice-theoretic description for parahoric subgroups using Bruhat-Tits theory in residue characteristic two, and apply them to define local models following the lead of Rapoport-Zink \cite{rapoport1996period} and Pappas-Rapoport \cite{pappas2009local}. In our case, there are two conjugacy classes of special parahoric subgroups. We show that the local models are smooth for the one class and normal, Cohen-Macaulay for the other class. We also prove that they represent the v-sheaf local models of Scholze-Weinstein. Under some additional assumptions, we obtain an explicit moduli interpretation of the local models. The second part of the thesis focuses on constructing integral models over $p=2$ for some Shimura varieties of abelian type with parahoric level structure, extending the previous work of Kim-Madapusi \cite{kim20162} and Kisin, Pappas, and Zhou \cite{kisin2018integral, kisin2024independenceellfrobeniusconjugacy, kisin2024integralmodelsshimuravarieties}. For Shimura varieties of Hodge type, we show that our integral models are canonical in the sense of Pappas-Rapoport \cite{pappas2021p}.
Read
