On a lifting problem of L-packets
On a lifting problem of L-packets
复制标题
关于L-包的提升问题
作者：
Bin Xu
设$G\subseteq \ widdetilde {G}$为特征为0的局部域上具有相同派生群的两个拟分裂连通的约化群。虽然一般来说l包的存在性仍然是推测性的，但我们认为$G$的l包应该是$\ widdetilde {G}$的l包的限制。基于此，我们希望从$G$的l包构造$\ widdetilde {G}$的l包。我们脑海中的主要例子是当$G=\text{Sp}(2n)$，其l包已由Arthur[表征的内镜分类：正交和对称群，Colloquium Publications, vol. 61 (American Mathematical Society, Providence， RI, 2013)]和$\ widdetilde {G}=\text{GSp}(2n)$确定。作为第一步，我们需要考虑l包的一些众所周知的推测性质。在本文中，我们展示了如何从推测性内窥镜理论推导出它们。作为应用，我们从$G$的l包中得到了$\ widdetilde {G}$的l包的一些结构信息。
Let $G\subseteq \widetilde{G}$ be two quasisplit connected reductive groups over a local field of characteristic zero and having the same derived group. Although the existence of L-packets is still conjectural in general, it is believed that the L-packets of $G$ should be the restriction of those of $\widetilde{G}$ . Motivated by this, we hope to construct the L-packets of $\widetilde{G}$ from those of $G$ . The primary example in our mind is when $G=\text{Sp}(2n)$ , whose L-packets have been determined by Arthur [The endoscopic classification of representations: orthogonal and symplectic groups, Colloquium Publications, vol. 61 (American Mathematical Society, Providence, RI, 2013)], and $\widetilde{G}=\text{GSp}(2n)$ . As a first step, we need to consider some well-known conjectural properties of L-packets. In this paper, we show how they can be deduced from the conjectural endoscopy theory. As an application, we obtain some structural information about L-packets of $\widetilde{G}$ from those of $G$ .
p-adic 场上 GLn 的当地 Langlands 对应
影响因子：
3.1
作者：
P. Scholze
通讯作者：
P. Scholze