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

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.

revised version of what used to be the second part of arXiv:2302.12747

References in corpus (12)

• Absolute prismatic cohomology
• The prismatization of $p$-adic formal schemes
• A $p$-adic Simpson correspondence for smooth proper rigid varieties
• Hodge--Tate prismatic crystals and Sen theory
• On the Hodge--Tate crystals over O_K
• Geometric Sen theory over rigid analytic spaces
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• Moduli spaces in $p$-adic non-abelian Hodge theory
• Hodge-Tate stacks and non-abelian $p$-adic Hodge theory of v-perfect complexes on rigid spaces
• v-vector bundles on $p$-adic fields and Sen theory via the Hodge-Tate stack