论文标题
shimura类型的Shimura品种的规范积分模型
Canonical integral models for Shimura varieties of toral type
论文作者
论文摘要
我们证明了PAPPA-Ropoport的猜想，即在Shimura品种由圆环定义的情况下，具有带有脊骨水平结构的Shimura品种的规范积分模型。作为一种重要成分，我们表明，使用Bhatt-Scholze Prismatic $ f $ -crystals的理论，有一个完全忠实的函数来自$ \ Mathcal {g} $ - 值的结晶代表gal $（\ bar {k}/k}/k}/k}/k）$ to $ \ \ \ \ \ \ \ \ \ \ \ {g} $ spd $ spd（o）其中$ \ mathcal {g} $是$ \ mathbb {z} _p $和$ \ mathcal {o} _k $是$ \ mathbb {z} _p {o} _k $是整数$ p $ adic field $ k $。
We prove the Pappas-Rapoport conjecture on the existence of canonical integral models of Shimura varieties with parahoric level structure in the case where the Shimura variety is defined by a torus. As an important ingredient, we show, using the Bhatt-Scholze theory of prismatic $F$-crystals, that there is a fully faithful functor from $\mathcal{G}$-valued crystalline representations of Gal$(\bar{K}/K)$ to $\mathcal{G}$-shtukas over Spd$(\mathcal{O}_K)$, where $\mathcal{G}$ is a parahoric group scheme over $\mathbb{Z}_p$ and $\mathcal{O}_K$ is the ring of integers in a $p$-adic field $K$.
