The overconvergence of multivariable $(\varphi_q,\mathcal{O}_K^{\times})$-modules at the perfectoid level

Changjiang Du

The overconvergence of multivariable $(\varphi_q,\mathcal{O}_K^{\times})$-modules at the perfectoid level

Number Theory 2026-03-04 v2

Authors: Changjiang Du

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 $(\varphi_q,\mathcal{O}_K^{\times})$ -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.

Keywords

overconvergence Fargues-Fontaine curve perfectoid multivariable module $\varphi_q$-module

Cite

@article{arxiv.2603.01704,
  title  = {The overconvergence of multivariable $(\varphi_q,\mathcal{O}_K^{\times})$-modules at the perfectoid level},
  author = {Changjiang Du},
  journal= {arXiv preprint arXiv:2603.01704},
  year   = {2026}
}

Comments

42 pages, minor corrections and typos fixed

Related papers

View all related →