Can we dream of a 1-adic Langlands correspondence?

TL;DR

This paper hypothesizes a unified 1-adic Langlands correspondence to explain observed uniformities in the p-adic Langlands program across different primes.

Contribution

It proposes the novel idea of a 1-adic Langlands correspondence as a unifying framework for p-adic Langlands results.

Findings

Observation of p-independence in p-adic Langlands constructions

Formulation of the 1-adic Langlands hypothesis

Potential explanation for uniformity across primes

Abstract

After observing that some constructions and results in the $p$-adic Langlands programme are somehow independent from $p$, we formulate the hypothesis that this astonishing uniformity could be explained by a 1-adic Langlands correspondence.