论文标题
超高的阿贝尔表面的准发育组通过亲欧塔尔基本组
Quasi-isogeny groups of supersingular abelian surfaces via pro-étale fundamental groups
论文作者
论文摘要
We consider a $J_b(\mathbb{Q}_p)$-torsor on the supersingular locus of the Siegel threefold constructed by Caraiani-Scholze, and show that it induces an isomorphism between a free group on a finite number of generators, and the group of self-quasi-isogenies of a supersingular abelian surface, respecting a principal polarization and a Prime至$ p $级别的结构。一路上，我们根据亲泰尔基本组对某些亲构型扭转进行了分类，描述了非正常方案的几何覆盖类别，并使用它来计算Pro-étale基本曲线群。
We consider a $J_b(\mathbb{Q}_p)$-torsor on the supersingular locus of the Siegel threefold constructed by Caraiani-Scholze, and show that it induces an isomorphism between a free group on a finite number of generators, and the group of self-quasi-isogenies of a supersingular abelian surface, respecting a principal polarization and a prime-to-$p$ level structure. Along the way, we classify certain pro-étale torsors in terms of the pro-étale fundamental group, describe the category of geometric covers of non-normal schemes, and use this to compute pro-étale fundamental groups of curves.
