$\mathbf{Spec}(\mathbb{Z})/\mathbb{F}_1$的坐标生成
The coordinate biring of $\mathbf{Spec}(\mathbb{Z})/\mathbb{F}_1$
摘要：
我们提出将$\mathbb{F}_1$ -代数定义为整双环，其上环结构是从$\mathbb{Z}$到$\mathbb{F}_1$的下降数据.则$\mathbf{Spec}(\mathbb{Z})/\mathbb{F}_1$的坐标双环是整线性递归序列的配Hadamard积的余环。我们将一个非交换模空间与此相关联，证明它是在$\mathbb{F}_1$上定义的，并且具有动机$\prod_{n \geq 0} \frac{s-n}{2 π}$。
英文摘要：
We propose to define $\mathbb{F}_1$-algebras as integral bi-rings with the co-ring structure being the descent data from $\mathbb{Z}$ to $\mathbb{F}_1$. The coordinate bi-ring of $\mathbf{Spec}(\mathbb{Z})/\mathbb{F}_1$ is then the co-ring of integral linear recursive sequences equipped with the Hadamard product. We associate a noncommutative moduli space to this setting, show that it is defined over $\mathbb{F}_1$, and has motive $\prod_{n \geq 0} \frac{s-n}{2 π}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
