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The Lange-Stuhler Theorem via Gerbes
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 GLn to group schemes over finite fields that are connected affine or of finite type.
Related
- Minimal Trivializing Isogenies of 𝔾m-gerbes over Abelian Varieties and Period-Index Problem
- Weak Lie 3-groups, 2-gerbes over torus fibrations of type F1, and T-Duality
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- Essential Dimension and Faithful Rank of Finite p-Gerbes
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BibTeX
@misc{zhang2026langestuhler,
title = {{The Lange-Stuhler Theorem via Gerbes}},
author = {Lei Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25665},
eprint = {2609.25665},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25665},
}
RIS
TY - UNPB
TI - The Lange-Stuhler Theorem via Gerbes
AU - Lei Zhang
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.25665
UR - https://arxiv.org/abs/2609.25665
AB - 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 GL_n to group schemes over finite fields that are connected affine or of finite type.
ER -