热带 adic 空间 I：拓扑半环的连续谱
代数几何
2024-07-24 v4 交换代数
环与代数
摘要
为构建 adic 空间的热带类比，我们研究某些素同余空间，作为拓扑环上连续赋值空间的一种拓扑半环替代。这需要建立拓扑幂等半环的理论，并以收敛幂级数半环为主要例子。我们通过在其上定义度量，将收敛幂级数半环视为拓扑空间。我们验证了在热带环面情形中，所提出的对象携带有意义的几何信息。特别地，我们证明了其维数表现符合预期。我们在后续论文中依据经典多面体几何给出了点的显式刻画。
引用
@article{arxiv.2209.15116,
title = {Tropical adic spaces I: The continuous spectrum of a topological semiring},
author = {Netanel Friedenberg and Kalina Mincheva},
journal= {arXiv preprint arXiv:2209.15116},
year = {2024}
}
备注
66 pages, 0 figures. A previous version has been split into two parts. The first part is the current version. The second part is now titled "Geometric interpretation of valuated term (pre)orders". The results are unchanged but some content has been rearranged; the presentation has been improved. Comments welcome!