论文标题
热带ADIC空间i：拓扑半程的连续光谱
Tropical adic spaces I: The continuous spectrum of a topological semiring
论文作者
论文摘要
为了建立ADIC空间的热带类似物，我们研究了某些主要一致性的空间，作为拓扑替代拓扑环的拓扑半置换替代品。这就需要构建拓扑结构的半能理论，我们将收敛功率序列的半序列视为一个主要例子。我们将收敛功率序列的半度性视为拓扑空间，通过定义标准。我们检查，在热带复曲面的情况下，提出的对象带有有意义的几何信息。特别是，我们表明尺寸的行为是预期的。在后续纸中，我们从经典的多面体几何形状方面给出了这些点的明确表征。
Towards building tropical analogues of adic spaces, we study certain spaces of prime congruences as a topological semiring replacement for the space of continuous valuations on a topological ring. This requires building the theory of topological idempotent semirings, and we consider semirings of convergent power series as a primary example. We consider the semiring of convergent power series as a topological space by defining a metric on it. We check that, in tropical toric cases, the proposed objects carry meaningful geometric information. In particular, we show that the dimension behaves as expected. We give an explicit characterization of the points in terms of classical polyhedral geometry in a follow up paper.
