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摘要翻译：
给出了半交换型指数微分方程的完全一阶理论。研究表明，这些理论也源于赫鲁晓夫斯基风格的一种带有预维度的融合结构。该理论包括一个方程组有解的充要条件。该必要条件将Ax微分域形式的Schanuel猜想推广到半交换型。半交换群的弱CIT是一个纯代数推论，它涉及代数子群与代数群的交集。
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英文标题：
《The theory of the exponential differential equations of semiabelian
varieties》
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作者：
Jonathan Kirby
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最新提交年份：
2009
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Logic 逻辑
分类描述：Logic, set theory, point-set topology, formal mathematics
逻辑，集合论，点集拓扑，形式数学
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英文摘要：
The complete first order theories of the exponential differential equations of semiabelian varieties are given. It is shown that these theories also arises from an amalgamation-with-predimension construction in the style of Hrushovski. The theory includes necessary and sufficient conditions for a system of equations to have a solution. The necessary condition generalizes Ax's differential fields version of Schanuel's conjecture to semiabelian varieties. There is a purely algebraic corollary, the "Weak CIT" for semiabelian varieties, which concerns the intersections of algebraic subgroups with algebraic varieties.
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PDF链接：
https://arxiv.org/pdf/0708.1352
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