Luqiao Xu

collaborators

2 papers

math.AG2026

Localization and Affine Schemes over $F_{1}$

Luqiao Xu

We develop the basic notions of commutative algebra and algebraic geometry over the field with one element $F_{1}$ , working within the Connes-Consani framework, which models…

math.AG2026

Hyper-Operations and Extension of Scalars from $F_{1}$ to $Z$

Luqiao Xu

The additive structure of $F_{1}$ -modules (in the sense of Segal's $I^$ -sets) differs fundamentally from that of abelian groups: addition is encoded through a family of $n$ -…

Localization and Affine Schemes over F1​

Hyper-Operations and Extension of Scalars from F1​ to Z

Localization and Affine Schemes over $F_{1}$

Hyper-Operations and Extension of Scalars from $F_{1}$ to $Z$