Absolute geometry and the Habiro topology

TL;DR

This paper explores the connections between different approaches to F1-geometry, the ABC-conjecture, and their implications for absolute geometry, aiming to unify diverse perspectives in number theory.

Contribution

It introduces a comparative analysis of Smirnov's and Borger's F1-geometry frameworks in relation to the ABC-conjecture and absolute geometry.

Findings

Identifies potential links between Smirnov's and Borger's F1-geometry approaches.

Provides insights into the role of F1-geometry in understanding the ABC-conjecture.

Suggests new directions for research in absolute geometry and number theory.

Abstract

Lecture notes of a course on A. Smirnov's approach to the ABC-conjecture via F1-geometry and an attempt to relate this to Jim Borger's F1-geometry based on lambda-rings.