The overconvergence of multivariable $(φ_q,\mathcal{O}_K^{\times})$-modules at the perfectoid level
Abstract
Let $K$ be a finite unramified extension of $\mathbb{Q}_p$, and $E$ a finite extension of $K$ with ring of integers $\mathcal{O}_E$. We define the overconvergence of multivariable $(φ_q,\mathcal{O}_K^{\times})$-modules over $A_{\mathrm{mv},E}$ and explore some basic properties. We prove the overconvergence at the perfectoid level using the geometry of relative Fargues-Fontaine curve.
Fields of Study & Subjects
Advanced Algebra and Geometry
Algebraic Geometry and Number Theory
Algebraic structures and combinatorial models
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 2 March 2026
- Language
- EN
- Document type
- Preprint