Dimension Polynomials of Intermediate Fields of Inversive Difference Field Extensions
Dimension Polynomials of Intermediate Fields of Inversive Difference Field Extensions
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反差分域扩展的中间域的维数多项式
DOI：
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发表时间：
2015
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通讯作者：
A. Levin
中科院分区：
文献类型：
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作者：
A. Levin
设K为逆差分场，L为K的有限生成的逆差分场扩展，F为该扩展的中间逆差分场。我们证明了一个数值多项式的存在性，并建立了它的性质和不变量，该多项式描述了由扩展L/K的自然过滤引起的F的过滤。然后引入了考虑其中间域链的可拓L/K的类型和维数概念。利用中间域的维数多项式的性质，得到了L/K的类型与维数之间的关系，以及该扩展的维数多项式所携带的差分双不变量。最后，我们将得到的结果推广到多元维多项式与给定的逆差分域扩展和基本平移集的划分相关的情况。
Let K be an inversive difference field, L a finitely generated inversive difference field extension of K, and F an intermediate inversive difference field of this extension. We prove the existence and establish properties and invariants of a numerical polynomial that describes the filtration of F induced by the natural filtration of the extension L/K associated with its generators. Then we introduce concepts of type and dimension of the extension L/K considering chains of its intermediate fields. Using properties of dimension polynomials of intermediate fields we obtain relationships between the type and dimension of L/K and difference birational invariants of this extension carried by its dimension polynomials. Finally, we present a generalization of the obtained results to the case of multivariate dimension polynomials associated with a given inversive difference field extension and a partition of the basic set of translations.