Model Theory with Applications to Algebra and Analysis: Counting and dimensions
Model Theory with Applications to Algebra and Analysis: Counting and dimensions
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模型理论及其在代数和分析中的应用：计数和维数
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
F. Wagner
中科院分区：
文献类型：
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作者：
E. Hrushovski;F. Wagner
我们证明了一个定理比较一个良好的尺寸概念的第二个，更基本的尺寸。专门针对非标准计数测度，它推广了Larsen和Pink关于簇与代数群的一般有限子群的交集的渐进上界的定理。作为第二个应用程序，我们将其应用到坏领域的积极特征，给一个渐近估计的数量的Fq-有理数点的一个可定义的乘法子群类似的Lang-Weil估计曲线在有限域。
We prove a theorem comparing a well-behaved dimension notion to a second, more rudimentary dimension. Specialising to a non-standard counting measure, this generalizes a theorem of Larsen and Pink on an asymptotic upper bound for the intersection of a variety with a general finite subgroup of an algebraic group. As a second application we apply this to bad fields of positive characteristic, to give an asymptotic estimate for the number of Fq-rational points of a definable multiplicative subgroup similar to the Lang-Weil estimate for curves over finite fields.