论文标题
Artin $ v $ stacks的Jacobian标准
A Jacobian Criterion for Artin $v$-stacks
论文作者
论文摘要
我们证明了Fargues-Scholze的Jacobian标准在Fargues-Fontaine曲线上平滑准标记品种的空间。也就是说，我们展示了如何使用其标准来推断出平滑ARTIN堆栈部分的类似物，该曲线通过线性代数组的作用来获得平滑的准标记品种的堆叠商来获得（示意图）fargues-fontaine曲线。作为一个应用程序，我们显示了在Fargues-Scholze几何Langlands计划中出现的各种Moduli堆栈，这在同时流畅的Artin $ v $堆栈上，并计算其$ \ ell $ dimensions。
We prove a generalization of the Jacobian criterion of Fargues-Scholze for spaces of sections of a smooth quasi-projective variety over the Fargues-Fontaine curve. Namely, we show how to use their criterion to deduce an analogue for spaces of sections of a smooth Artin stack over the (schematic) Fargues-Fontaine curve obtained by taking the stack quotient of a smooth quasi-projective variety by the action of a linear algebraic group. As an application, we show various moduli stacks appearing in the Fargues-Scholze geometric Langlands program are cohomologically smooth Artin $v$-stacks and compute their $\ell$-dimensions.
