蓝图-绝对算术？
Blueprints - towards absolute arithmetic?
摘要：
发展$\F_1$ -几何的动力之一是希望将Weil对黎曼假设的证明从正特征转化到数域上，这可能导致经典黎曼假设的证明。其基本思想是$\Z$的谱应该被解释为$\F_1$上的曲线，它具有类似于有限域上的曲线的完备$\bar{\Spec\Z}$。希望是，在算术表面$\bar{\Spec\Z} \times \bar{\Spec\Z}$上的除数的相交理论将允许模仿韦尔的证明。事实证明，可以从蓝图的角度定义具有某些属性的对象$\bar{\Spec\Z}$，这些属性在积极特征上接近其类似物的属性。这将在下面的笔记中解释，这是2012年3月在马克斯普朗克研究所发表的演讲的摘要。
英文摘要：
One of the driving motivations to develop $\F_1$-geometry is the hope to translate Weil's proof of the Riemann hypothesis from positive characteristics to number fields, which might result in a proof of the classical Riemann hypothesis. The underlying idea is that the spectrum of $\Z$ should find an interpretation as a curve over $\F_1$, which has a completion $\bar{\Spec\Z}$ analogous to a curve over a finite field. The hope is that intersection theory for divisors on the arithmetic surface $\bar{\Spec\Z} \times \bar{\Spec\Z}$ will allow to mimic Weil's proof. It turns out that it is possible to define an object $\bar{\Spec\Z}$ from the viewpoint of blueprints that has certain properties, which come close to the properties of its analogs in positive characteristic. This shall be explained in the following note, which is a summary of a talk given at the Max Planck Institute in March, 2012.
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。
