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arXiv · 2511.15126

$G$-gerbes on perfectoid spaces

Xiaohuan Long·Yibin Wang·Xiangdong Wu·Ru Yi
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Abstract

Let $K$ be a complete non-archimedean field over $\mathbb{Q}_p$, $G$ be a rigid group over $K$, and $X$ be a perfectoid space over $K$. We consider the natural morphism of sites $\nu: X_v \to X_{\mathrm{\acute{e}t}}$. It is known from work of Heuer that the direct image functor $\nu_*$ induces an equivalence of the categories of $G$-torsors. In this article, we show that there is an equivalence of 2-categories of $G$-gerbes on these two topologies.

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Xiaohuan Long, Yibin Wang, Xiangdong Wu, Ru Yi. 2025-11-19. $G$-gerbes on perfectoid spaces. https://arxiv.org/abs/2511.15126

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