Perfectoid C_i transfer

2025/04/20 by Kartas, Konstantinos
#Algebraic Geometry (math.AG) #FOS: Mathematics #Logic (math.LO) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2504.14719

Abstract

We prove a perfectoid analogue of the Ax-Kochen theorem on zeros of p-adic forms: Given d∈ ℕ, there is a finite totally ramified extension E/ℚ_p such that every untilt of \mathbbF_p( (t^1/p^∞) ) containing E is C₂(d). We also prove a similar result for the existence of rational points in rationally connected varieties over perfectoid field extensions of ℚ_p^ur.

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