论文标题
在线性AFL上：非基本情况
On the Linear AFL: The Non-Basic Case
论文作者
论文摘要
线性算术基本引理（AFL）的猜想比较了乙二醇变形空间上的相交数量与轨道积分的衍生物。它是针对Arxiv中的椭圆轨道引入的：1803.07553和Arxiv：2010.07365。在这些情况下，针对基本的同学类别提出了相关的交叉问题。在本文中，我们将理论扩展到所有轨道和所有同等基础类别。我们的主要结果是将AFL的非基础病例减少到基本案例中，这是通过利用连接的étale序列来实现的。我们的理论将在全球环境中相关，在全球环境中，本地非椭圆形轨道也可能以非平凡的方式做出贡献。
The linear Arithmetic Fundamental Lemma (AFL) conjecture compares intersection numbers on Lubin--Tate deformation spaces with derivatives of orbital integrals. It has been introduced for elliptic orbits in arXiv:1803.07553 and arXiv:2010.07365. In these cases, the relevant intersection problem is formulated for the basic isogeny class. In the present article, we extend the theory to all orbits and all isogeny classes. Our main result is a reduction of the non-basic cases of the AFL to the basic ones, which is achieved by exploiting the connected-étale sequence. Our theory will be relevant in the global setting, where also locally non-elliptic orbits may contribute in a non-trivial way.
