p-adic域中的多面体与单形

摘要：

我们引入拓扑概念的多面体和单纯形，后者被期望在p-adically封闭领域中发挥的作用，真正的单纯形在经典的三角剖分的半代数集的实封闭的领域。我们证明了每一个p-adic多面体的面是多面体，他们形成一个有根树的专业化。然后将单纯形定义为面树为链的多面体。我们的主要结果是一个建设允许划分每一个p-adic多面体在一个复杂的p-adic单形与规定的脸和形状。

英文摘要：

We introduce topological notions of polytopes and simplexes, the latter being expected to play in p-adically closed fields the role played by real simplexes in the classical results of triangulation of semi-algebraic sets over real closed fields. We prove that the faces of every p-adic polytope are polytopes and that they form a rooted tree with respect to specialisation. Simplexes are then defined as polytopes whose faces tree is a chain. Our main result is a construction allowing to divide every p-adic polytope in a complex of p-adic simplexes with prescribed faces and shapes.

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