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

Yijun Yuan

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arXiv · 2511.17029

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

Yijun Yuan

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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.

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Yijun Yuan. 2025-11-21. Descent of $(\varphi,\tau)$-modules in characteristic $p$. https://arxiv.org/abs/2511.17029

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