论文标题
$ \ mathrm {sl} _2 $ -Eigenvarieties上的内窥镜检查
Endoscopy on $\mathrm{SL}_2$-eigenvarieties
论文作者
论文摘要
在本文中，我们研究了$ \ mathrm {sl} _2 $在完全真实的领域上的p-adic内窥镜检查，从几何角度来看。我们表明，定期体重的内窥镜L弹丸的非自动形态成员为特征性征收特征向量导致了特征性的内窥镜内镜面的过度共同点，我们精确地量化了这一贡献。这给出了第二作者的先前工作的新观点。我们的方法是几何的，基于表明$ \ mathrm {sl} _2 $ -Eigenvariety在本地是本地的特征值商的商，$ \ mathrm {gl} _2 $，它使我们可以明确地描述$ \ m m i \ nathrm {sl} _2 $ -egar} _2 $ -EIGER-eigig-eigig-eigigegar-eigigegar-eigigegar}特别是，我们表明它通常在这样的地方不可能成为戈伦斯坦。
In this paper, we study p-adic endoscopy on eigenvarieties for $\mathrm{SL}_2$ over totally real fields, taking a geometric perspective. We show that non-automorphic members of endoscopic L-packets of regular weight contribute eigenvectors to overconvergent cohomology at critically refined endoscopic points on the eigenvariety, and we precisely quantify this contribution. This gives a new perspective on and generalizes previous work of the second author. Our methods are geometric, and are based on showing that the $\mathrm{SL}_2$-eigenvariety is locally a quotient of an eigenvariety for $\mathrm{GL}_2$, which allows us to explicitly describe the local geometry of the $\mathrm{SL}_2$-eigenvariety. In particular, we show that it often fails to be Gorenstein at such points.
