Complete flags on flat vector bundles in positive characteristic

2025/03/17 by Youhei Morita, Morita, Yohei, Yasuhiro Wakabayashi +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.2503.13750

arxiv created 2026/07/31 · arxiv updated 2026/08/03

Abstract

Let X be a connected, smooth, and projective curve of genus g over an algebraically closed field of characteristic p >0. This paper investigates a characteristic-p analogue of a well-known fact concerning flat vector bundles in characteristic 0. That is to say, we prove that the inequality g ≤ 1 holds if and only if any flat vector bundle on X admits a complete flag. We also explore a generalization of this result in a broader setting.

Related

• Formal orbifolds and orbifold bundles in positive characteristic
• Geometric Height on Flag Varieties in Positive Characteristic
• On flat bundles in characteristic 0 and p>0
• Vector Bundles on Flag varieties
• Cleanliness and log-characteristic cycles for vector bundles with flat connections