论文标题
在当地的整体Shimura品种上
On integral local Shimura varieties
论文作者
论文摘要
我们提供了“本地Shimura品种”的构造，该方案概括了Drinfeld $ p $ - 亚洲上半部分的众所周知的积分模型。该构建适用于所有古典团体，至少适用于奇数$ p $。这些正式方案还概括了由Rapoport-Zink通过$ P $可分组组定义的正式方案，并且纯粹以群体理论术语为特征。更确切地说，对于本地$ p $ -adic shimura datum $（g，b，μ）$和准帕拉克组方案$ \ mathcal g $ for $ g $，Scholze已在参数$ p $ - adic shtukas上定义了一个函数。他猜想该函子由正式的正式方案表示，该方案在有限的类型上正式正式，并且超过$ o _ {\ breve e} $。当使用Rapoport-Zink正式方案使用$（g，b，μ）$是（p）EL类型时，Scholze-Weinstein证明了这一猜想。当$ p \ neq 2 $时，当$ p = 2 $和$ g $的任何$（g，μ）$的Abelian类型中，我们证明了这种猜想。我们还将这种形式方案的通用纤维与局部Shimura品种联系起来，Scholze附加到$（G，B，μ，{\ Mathcal G}）$的刚性分析空间。
We give a construction of "integral local Shimura varieties" which are formal schemes that generalize the well-known integral models of the Drinfeld $p$-adic upper half spaces. The construction applies to all classical groups, at least for odd $p$. These formal schemes also generalize the formal schemes defined by Rapoport-Zink via moduli of $p$-divisible groups, and are characterized purely in group-theoretic terms. More precisely, for a local $p$-adic Shimura datum $(G, b, μ)$ and a quasi-parahoric group scheme $\mathcal G$ for $G$, Scholze has defined a functor on perfectoid spaces which parametrizes $p$-adic shtukas. He conjectured that this functor is representable by a normal formal scheme which is locally formally of finite type and flat over $O_{\breve E}$. Scholze-Weinstein proved this conjecture when $(G, b, μ)$ is of (P)EL type by using Rapoport-Zink formal schemes. We prove this conjecture for any $(G, μ)$ of abelian type when $p\neq 2$, and when $p=2$ and $G$ is of type $A$ or $C$. We also relate the generic fiber of this formal scheme to the local Shimura variety, a rigid-analytic space attached by Scholze to $(G, b, μ, {\mathcal G})$.
