${\mathbb{F}}_1$ for everyone

Abstract

This text serves as an introduction to ${\mathbb{F}}_1$-geometry for the general mathematician. We explain the initial motivations for ${\mathbb{F}}_1$-geometry in detail, provide an overview of the different approaches to ${\mathbb{F}}_1$ and describe the main achievements of the field.

overview paper for the general mathematician; 31 pages

References in corpus (5)

• New Approach to Arakelov Geometry
• Lambda-rings and the field with one element
• Algebraic groups over the field with one element
• Algebraic Geometry Over Hyperrings
• Compactifying Spec Z

Cited by in corpus (1)

• Lift of fractional D-brane charge to equivariant Cohomotopy theory