A taste of Weil theory in characteristic one

TL;DR

This paper provides an introductory exploration of the arithmetic theory of the field with one element, $\

Contribution

It offers initial sketches and visualizations of Weil theory concepts in characteristic one, advancing foundational understanding.

Findings

Preliminary ideas on Weil theory in characteristic one

Visual representations of arithmetic structures in $\

Initial conceptual framework for $\

Abstract

In this very short and sketchy chapter, we draw some pictures on the arithmetic theory of $\mathbb{F}_1$.