F1-schemes and toric varieties

TL;DR

This paper explores the relationship between F1-schemes and toric varieties, establishing that integral F1-schemes of finite type are essentially toric varieties and discussing related concepts like etale morphisms and the F1-zeta function.

Contribution

It demonstrates that integral F1-schemes of finite type are equivalent to toric varieties and connects the F1-zeta function with toric geometry.

Findings

Integral F1-schemes of finite type are equivalent to toric varieties.

Introduces etale morphisms and universal coverings for F1-schemes.

Provides a description of the F1-zeta function using toric geometry.

Abstract

This paper contains a loose collection of remarks on F1-schemes. Etale morphisms and universal coverings are introduced. The relation to toric varieties, at least for integral schemes, is clarified.In this paper it is shown that integral F1-schemes of finite type are essentially the same as toric varieties. A description of the F1-zeta function in terms of toric geometry is given. Etale morphisms and universal coverings are introduced.