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arXiv · 1711.08162

Base change of twisted Fontaine-Faltings modules and Twisted Higgs-de Rham flows over very ramified valuation rings

Ruiran Sun·Jinbang Yang·Kang Zuo
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Abstract

In this short notes, we prove a stronger version of Theorem 0.6 in our previous paper arXiv:1709.01485: Given a smooth log scheme $(\mathcal{X} \supset \mathcal{D})_{W(\mathbb{F}_q)}$, each stable twisted $f$-periodic logarithmic Higgs bundle $(E,\theta)$ over the closed fiber $(X \supset D)_{\mathbb{F}_q}$ will correspond to a $\mathrm{PGL}_r(\mathbb{F}_{p^f})$-crystalline representation of $\pi_1((\mathcal{X} \setminus \mathcal{D})_{W(\mathbb{F}_q)[\frac{1}{p}]})$ such that its restriction to the geometric fundamental group is absolutely irreducible.

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Ruiran Sun, Jinbang Yang, Kang Zuo. 2017-11-22. Base change of twisted Fontaine-Faltings modules and Twisted Higgs-de Rham flows over very ramified valuation rings. https://arxiv.org/abs/1711.08162

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