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arXiv · 2409.05073

Parahoric reduction theory of formal connections (or Higgs fields)

Zhi Hu·Pengfei Huang·Ruiran Sun·Runhong Zong
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Abstract

In this paper, we establish the parahoric reduction theory of formal connections (or Higgs fields) on a formal principal bundle with parahoric structures, which generalizes Babbitt-Varadarajan's result for the case without parahoric structures [5] and Boalch's result for the case of regular singularity [9]. As applications, we prove the equivalence between extrinsic definition and intrinsic definition of regular singularity and provide a criterion of relative regularity for formal connections, and also demonstrate a parahoric version of Frenkel-Zhu's Borel reduction theorem of formal connections [23].

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Zhi Hu, Pengfei Huang, Ruiran Sun, Runhong Zong. 2024-09-08. Parahoric reduction theory of formal connections (or Higgs fields). https://arxiv.org/abs/2409.05073

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