论文标题
Équationspour le le premierrevêtementde l'espacesymétriquede drinfeld
Équations pour le premier revêtement de l'espace symétrique de Drinfeld
论文作者
论文摘要
这项工作的目的是研究德林菲尔德塔的第一个封面$σ^1 $的几何形状的某些方面，超过$ \ mathbb {h}^d_k $ the $ k $ $ k $ $ \ mathbb {q} Q}} _p $的drinfeld对称空间。这是订单prime的循环范围，即$ p $，甚至是kummer类型的$ \ mathbb {h}^d_k $从作者先前的作品中显示的。然后，通过kummer精确序列在$ \ mathbb {h}^d_k $上在$ \ mathbb {h}^d_k $上完全描述它，本文的主要结果给出了此类的明确描述，从而为$σ^1 $提供了“方程式”。该语句在Wang获得的顶点上扩展并至关重要的是（最初是由Teitelbaum在Dimension 1中获得的）。我们全局方程式的主要结果之一是$ \ mathbb {h}^d_k $的可逆函数的可逆函数的描述。
The goal of this work is to study some aspects of the geometry of the first cover $Σ^1$ in the Drinfeld tower over $\mathbb{H}^d_K$ the Drinfeld symmetric space over $K$ a finite extension of $\mathbb{Q}_p$. It is a cyclic étale cover of order prime to $p$ and even of Kummer type from the vanishing of the Picard group of $\mathbb{H}^d_K$ shown in a previous work of the author. It is then completely described by a certain class of invertible functions on $\mathbb{H}^d_K$ via the Kummer exact sequence and the main result of this article gives an explicit description of this class thus providing "equations" for $Σ^1$. This statement extends and uses crucially the local description over a vertex obtained by Wang (and originally by Teitelbaum in dimension 1). One of the main consequence of our global equation is the description of invertible functions of $Σ^1$ in terms of the invertible functions of $\mathbb{H}^d_K$.
