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<p>We introduce the concept of parabolic bases to establish a localized framework for parabolic bundles and parabolic λ-connections. Building on this foundation, we propose a novel method for constructing the parabolic non-abelian Hodge correspondence in positive characteristic, extending the work originally developed by Krishnamoorthy and Sheng (2020) for algebraic curves. Additionally, we investigate the rank 2 parabolic Higgs-de Rham flow operator and present a modified version of the Sun-Yang-Zuo algorithm, specifically adapted to the parabolic setting.</p>

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Constructing parabolic non-Abelian Hodge correspondence in positive characteristic using parabolic bases

  • 期刊论文

  • 发表日期：

    2025年6月5日

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  • Xiaojin Lin

摘要

We introduce the concept of parabolic bases to establish a localized framework for parabolic bundles and parabolic λ-connections. Building on this foundation, we propose a novel method for constructing the parabolic non-abelian Hodge correspondence in positive characteristic, extending the work originally developed by Krishnamoorthy and Sheng (2020) for algebraic curves. Additionally, we investigate the rank 2 parabolic Higgs-de Rham flow operator and present a modified version of the Sun-Yang-Zuo algorithm, specifically adapted to the parabolic setting.