通过格布证明的 Lange-Stuhler 定理

中文摘要 AI 辅助

我们将 Lange-Stuhler 定理重新表述为分类栈的 2-笛卡尔方块的泛性质。这一表述表明，在特征 p>0 的任意纤维范畴上，每个秩为 r 的 Frobenius 周期向量丛都被一个有限平展 torsor 平凡化，无需几何假设或对基域除特征外的限制。该构造从 GL_n 推广到有限域上连通仿射或有限型的群概形。

英文摘要

We recast the Lange-Stuhler theorem as the universal property of a $2$-cartesian square of classifying stacks. This formulation shows that every Frobenius-periodic vector bundle of rank $r$ on an arbitrary fibered category in characteristic $p>0$ is trivialized by a finite étale torsor, without geometric hypotheses or restrictions on the ground field beyond its characteristic. The construction extends from $\mathrm{GL}_n$ to group schemes over finite fields that are connected affine or of finite type.

发表机构

• Sun Yat-Sen University（中山大学）

机构由 AI 辅助整理，请以论文原文为准。