论文标题
西加尔的伽马环和通用算术
Segal's Gamma rings and universal arithmetic
论文作者
论文摘要
西加尔的伽马环为绝对代数几何形状提供了自然框架。我们使用Almkvist的全球Witt构造来探索与J. Borger F1 - 几何形态的关系，并计算AlmkVist的Witt Founctor-ring作为最简单的伽马环S。我们证明，它对Galois与BC-System的Galois不变的一部分是同构的，并展示了Lambda-rambda-rings and arbict and arthmcity and ar arthmmets and arthmcity。然后，我们集中于Z的Arakelov紧凑型，该Z获得了S-Elgebras的结构。在提供了分裂d的经典theta不变性的概率解释之后，我们展示了如何与d的伽马空间相关联，该伽马空间以同义术语编码D. D.的Riemann-Roch问题。
Segal's Gamma-rings provide a natural framework for absolute algebraic geometry. We use Almkvist's global Witt construction to explore the relation with J. Borger F1-geometry and compute the Witt functor-ring of Almkvist for the simplest Gamma-ring S. We prove that it is isomorphic to the Galois invariant part of the BC-system, and exhibit the close relation between Lambda-rings and the Arithmetic site. Then, we concentrate on the Arakelov compactification of Z which acquires a structure sheaf of S-algebras. After supplying a probabilistic interpretation of the classical theta invariant of a divisor D, we show how to associate to D a Gamma-space that encodes, in homotopical terms, the Riemann-Roch problem for D.
