arXiv 1909.090482019-09-19math.AGmath.FAmath.LO

非阿基米德局部域上C-exp类分布的WF-完整性

WF-holonomicity of C-exp-class distributions on non-archimedean local fields

Avraham Aizenbud, Raf Cluckers

摘要：

在几何和非阿基米德局部域分析的背景下，研究了文献[11]中的$C^{\mathrm exp}$类分布和文献[1]中的WF-完整性概念，证明了任何$C^{\mathrm exp}$类分布都是WF-完整的.这样，我们就回答了[1]中的一个问题，给出了一个非阿基米德局部域的WF-完整分布的框架，它在傅里叶变换下是稳定的，并且包含了许多自然分布，特别是[1]中研究的分布。我们进一步表明，可以正则化分布，而不离开$C^{\mathrm exp}$类。最后，通过证明[11]的一个结果的逆命题，证明了$C^{\mathrm exp}$类函数和分布的零轨迹与光滑轨迹之间的密切联系.一个关键的成分是一个新的决议结果子解析函数（通过修改），嵌入决议的解析函数和模型论的基础上。

英文摘要：

In the context of geometry and analysis on non-archimedean local fields, we study two recent notions, $C^{\mathrm exp}$-class distributions from [11] and WF-holonomicity from [1], and we show that any distribution of $C^{\mathrm exp}$-class is WF-holonomic. Thus we answer a question from [1] by providing a framework of WF-holonomic distributions for non-archimedean local fields which is stable under taking Fourier transforms and which contains many natural distributions, in particular, the distributions studied in [1]. We further show that one can regularize distributions without leaving the $C^{\mathrm exp}$-class. Finally, we show a close link between zero loci and smooth loci for functions and distributions of $C^{\mathrm exp}$-class, by proving a converse to a result of [11]. A key ingredient is a new resolution result for subanalytic functions (by alterations), based on embedded resolution for analytic functions and model theory.

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