论文标题
Aggine Deligne-lusztig品种的连接组件
The connected components of affine Deligne--Lusztig varieties
论文作者
论文摘要
我们计算了任意旁学水平的连接组件仿射deligne- lusztig品种和局部的shimura品种，从而完全普遍地解决了在\ cite {he}中提出的猜想（即使对于非quasisplit组）。我们通过将它们与$ p $ -Adic shtukas的无限级模量空间的连接组件联系起来，从而实现这一目标，在这里我们使用v-sheaf理论技术，例如\ textit {kimberlites}的专业化图。一路上，我们给出了$ p $ addic hodge的理论特征。 作为应用，我们获得了许多在任意脊椎动物水平的Shimura品种积分模型的几何形状的结果。特别是，我们推断出在任意连接的脊柱旁水平的准切片组的Shimura品种的积分模型上，推断出新的CM提升结果。
We compute the connected components of arbitrary parahoric level affine Deligne--Lusztig varieties and local Shimura varieties, thus resolving the conjecture raised in \cite{He} in full generality (even for non-quasisplit groups). We achieve this by relating them to the connected components of infinite level moduli spaces of $p$-adic shtukas, where we use v-sheaf-theoretic techniques such as the specialization map of \textit{kimberlites}. Along the way, we give a $p$-adic Hodge-theoretic characterization of HN-irreducibility. As applications, we obtain many results on the geometry of integral models of Shimura varieties at arbitrary parahoric levels. In particular, we deduce new CM lifting results on integral models of Shimura varieties for quasi-split groups at arbitrary connected parahoric levels.
