Parabolic Crystalline Representations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908497552080896 |
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| author | Liu, Zhenmou Yang, Jinbang Zuo, Kang |
| author_facet | Liu, Zhenmou Yang, Jinbang Zuo, Kang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_10449 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Parabolic Crystalline Representations Liu, Zhenmou Yang, Jinbang Zuo, Kang Algebraic Geometry 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. |
| title | Parabolic Crystalline Representations |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2309.10449 |