Descent of $(\varphi,\tau)$-modules in characteristic $p$

Yijun Yuan

Descent of $(\varphi,\tau)$-modules in characteristic $p$

Number Theory 2025-11-24 v1

Authors: Yijun Yuan

Abstract

In this article, we study the descent of $(\varphi,\tau)$ -modules over perfectoid period rings in characteristic $p$ via Berger and Rozensztajn's theory of super-H\"{o}lder vectors. This is a generalization of their work on $(\varphi,\Gamma)$ -modules. As an application, we answer a question of Caruso regarding the connection between $(\varphi,\tau)$ -modules and $(\varphi,\Gamma)$ -modules without involving Galois representations as intermediaries.

Keywords

$(\varphi,\tau)$-modules perfectoid rings descent theory super-H"{o}lder vectors $(\varphi,\Gamma)$-modules

Cite

@article{arxiv.2511.17029,
  title  = {Descent of $(\varphi,\tau)$-modules in characteristic $p$},
  author = {Yijun Yuan},
  journal= {arXiv preprint arXiv:2511.17029},
  year   = {2025}
}

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17 pages

Descent of $(\varphi,\tau)$-modules in characteristic $p$

Abstract

Keywords

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