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arXiv · 2309.10449

Parabolic Crystalline Representations

Zhenmou Liu·Jinbang Yang·Kang Zuo
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Abstract

The theory of crystalline representations was established by Fontaine and Laffaille, Faltings, and others. In this paper, we develop a parabolic version of this theory. The key point is the construction of the parabolic version of Fontaine-Faltings modules and Faltings' $\mathbb D$-functor. The theory of Higgs-de Rham flows can be used to efficiently construct crystalline representations. We have established a parabolic version and utilized it to construct infinitely many crystalline representations. The twisted versions discussed in Sun, Yang, and Zuo's work can be seen as a special case, where the parabolic weights are equal at every infinity point.

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Zhenmou Liu, Jinbang Yang, Kang Zuo. 2025-08-22. Parabolic Crystalline Representations. https://arxiv.org/abs/2309.10449

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