Mathematical Sciences: Rigid Analytic Geometry and Logic

数学科学：刚性解析几何和逻辑

• 批准号: 9401451
• 负责人: Leonard Lipshitz
• 金额: $ 22.7万
• 依托单位: Purdue Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-15 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401451&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Rigid; Analytic; Geometry

9401451 Lipshitz L. Lipshitz, Z. Robinson and their students will continue their investigation of rigid subanalytic and semianalytic sets (i.e. subanalytic and semianalytic sets over an algebraically closed field which is complete with respect to a non-Archimedean absolute value). This investigation will entail further work on the algebra and geometry of the rings of separated power series. Among other topics, they will investigate unique factorization, uniformization, Stein factorization, the singular locus theorem, and sheaf theory over these rings. Methods to be used will be nonstandard models and quantifier elimination from mathematical logic, together with techniques from commutative algebra and algebraic geometry. The sets of points in real space defined by systems of equations and inequalities among analytic functions are called analytic sets. The projection (i.e. the shadow) of such a set on a lower dimensional subspace is called subanalytic. Real subanalytic sets arise in several branches of mathematics, such as differential equations and geometry. Similar classes of sets arise naturally, for example in number theory, over fields different from the real numbers, where the notion of distance has rather different properties. These sets, however, share many of the nice properties of their real cousins. Lipshitz, Robinson and their students will continue their investigation of the properties of these sets, using methods from mathematical logic, commutative algebra and algebraic geometry. ***

小行星9401451 L. Lipshitz，Z.罗宾逊和他们的学生将继续他们的调查刚性subanalytic和semianalytic集（即subanalytic和semianalytic集在一个代数闭域是完整的关于非阿基米德绝对值）。 这项调查将需要进一步的工作代数和几何环的分离幂级数。 在其他主题中，他们将调查独特的因式分解，均匀化，斯坦因式分解，奇异轨迹定理，并在这些环层理论。 方法将使用非标准模型和量词消除从数学逻辑，连同技术从交换代数和代数几何。 由解析函数之间的方程组和不等式定义的真实的空间中的点的集合称为解析集。 这样的集合在低维子空间上的投影（即阴影）称为次解析的。 真实的次解析集出现在数学的几个分支中，例如微分方程和几何。 类似的集合类自然出现，例如在数论中，在不同于真实的数的域上，距离的概念具有相当不同的性质。 然而，这些集合与它们的真实的表亲有许多共同的好特性。 Lipshitz，罗宾逊和他们的学生将继续他们的调查性质，这些集，使用的方法，从数理逻辑，交换代数和代数几何。 ***