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arXiv · 2312.07554

The small $p$-adic Simpson correspondence in terms of moduli spaces

Johannes Anschütz·Ben Heuer·Arthur-César Le Bras
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Abstract

For any rigid space over a perfectoid extension of $\mathbb Q_p$ that admits a liftable smooth formal model, we construct an isomorphism between the moduli stacks of Hitchin-small Higgs bundles and Hitchin-small v-vector bundles. This constitutes a moduli-theoretic improvement of the small $p$-adic Simpson correspondence of Faltings, Abbes-Gros, Tsuji and Wang. Our construction is based on the Hodge-Tate stack of Bhatt-Lurie. We also prove an analogous correspondence in the arithmetic setting of rigid spaces of good reduction over $p$-adic fields.

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Johannes Anschütz, Ben Heuer, Arthur-César Le Bras. 2023-12-07. The small $p$-adic Simpson correspondence in terms of moduli spaces. https://arxiv.org/abs/2312.07554

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