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arXiv · 2609.25665

The Lange-Stuhler Theorem via Gerbes

Lei Zhang
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Abstract

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.

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Lei Zhang. 2026-09-22. The Lange-Stuhler Theorem via Gerbes. https://arxiv.org/abs/2609.25665

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