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arXiv · 2504.14719

Perfectoid $C_i$ transfer

Konstantinos Kartas
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Abstract

We prove a perfectoid analogue of the Ax-Kochen theorem on zeros of $p$-adic forms: Given $d\in \mathbb{N}$, there is a finite totally ramified extension $E/\mathbb{Q}_p$ such that every untilt of $\mathbb{F}_p(\!(t^{1/p^{\infty}})\!)$ containing $E$ is $C_2(d)$. We also prove a similar result for the existence of rational points in rationally connected varieties over perfectoid field extensions of $\mathbb{Q}_p^{ur}$.

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Konstantinos Kartas. 2025-04-20. Perfectoid $C_i$ transfer. https://arxiv.org/abs/2504.14719

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