论文标题
估值格子和光谱
Valuative lattices and spectra
论文作者
论文摘要
本文的第一部分是关于使用动态理论和动力学代数结构设计的动态构建方法的调查。动力学方法可为经典数学的众多抽象对象揭示隐藏的计算内容，这似乎是一种先验的建设性，例如（离散）字段的代数闭合。当经典数学中的证明使用这些抽象对象并产生具体结果时，动态方法通常可以发现该混凝土结果的算法。本文的第二部分将这种动力学方法应用于划分理论。我们比较了文献中存在的两个评估光谱概念，并引入了第三个概念，这在专门介绍了代数封闭离散有价值领域的动态理论的文章中隐含。这两个概念分别是由于Huber \＆Knebusch和Coquand引起的。我们证明，相应的估值格子基本相同。我们建立了与这些理论相对应的正式Valuativestellensätze，并比较了所产生的估值维度的概念。
The first part of the present article consists in a survey about the dynamical constructive method designed using dynamical theories and dynamical algebraic structures. Dynamical methods uncovers a hidden computational content for numerous abstract objects of classical mathematics, which seem a priori inaccessible constructively, e.g., the algebraic closure of a (discrete) field. When a proof in classical mathematics uses these abstract objects and results in a concrete outcome, dynamical methods generally make possible to discover an algorithm for this concrete outcome. The second part of the article applies this dynamical method to the theory of divisibility. We compare two notions of valuative spectra present in the literature and we introduce a third notion, which is implicit in an article devoted to the dynamical theory of algebraically closed discrete valued fields. The two first notions are respectively due to Huber \& Knebusch and to Coquand. We prove that the corresponding valuative lattices are essentially the same. We establish formal Valuativestellensätze corresponding to these theories, and we compare the various resulting notions of valuative dimensions.
