Tropical geometry over the tropical hyperfield
Tropical geometry over the tropical hyperfield
复制标题
热带超场上的热带几何
DOI：
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发表时间：
2019
影响因子：
0.8
通讯作者：
Oliver Lorscheid
中科院分区：
文献类型：
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作者：
Oliver Lorscheid
在本文中，我们将热带超场的思想与有序蓝图理论相结合，给出了热带方案理论的新表述。关键的见解是非阿基米德绝对值可以被视为热带超场的态射。反过来，有序的蓝图使得考虑经典品种到热带超领域的基础变化成为可能。我们将这种基础变化称为经典品种的方案理论热带化。
我们的第一个主要结果将经典品种的贝尔科维奇分析和热带化描述为方案理论热带化的理性点集，包括各自拓扑的表征。我们的第二个主要结果表明，Giansiracusa 弯曲关系可以通过方案理论热带化的自然构造得出。
In this text, we merge ideas around the tropical hyperfield with the theory of ordered blueprints to give a new formulation of tropical scheme theory. The key insight is that a nonarchimedean absolute value can be considered as a morphism into the tropical hyperfield. In turn, ordered blueprints make it possible to consider the base change of a classical variety to the tropical hyperfield. We call this base change the scheme theoretic tropicalization of the classical variety.
Our first main result describes the Berkovich analytification and the tropicalization of a classical variety as sets of rational points of scheme theoretic tropicalizations, including a characterization of the respective topologies. Our second main result shows that the Giansiracusa bend relations can be derived by a natural construction from the scheme theoretic tropicalization.
影响因子：
2.5
作者：
Jeffrey Giansiracusa;Noah Giansiracusa
通讯作者：
Jeffrey Giansiracusa;Noah Giansiracusa