The relativistic $p$-adic sunscreen conjecture

TL;DR

This paper proposes a conjecture concerning the intersection properties of the Banach-Colmez space with germs of smooth rigid analytic curves in a p-adic setting.

Contribution

It introduces a new conjecture linking p-adic Banach spaces and rigid analytic geometry, expanding understanding of their intersection behavior.

Findings

Formulated a new conjecture about intersections in p-adic geometry.

Connected Banach-Colmez spaces with rigid analytic curves.

Provides a framework for future research in p-adic intersection theory.

Abstract

We formulate a conjecture about intersections between the Banach-Colmez space $\mathrm{BC}(1/2)$ and germs of smooth rigid analytic curves at the origin in $\mathbb{A}^2_{\mathbb{C}_p}$