洛朗级数代数在形式幂级数领域的支持
Support of Laurent series algebraic over the field of formal power series
摘要：
本文研究了特征零域上的幂级数环上的多元洛朗级数的代数支撑。我们的第一个结果是这样的洛朗级数的支撑的一种极大对偶锥的存在性。作为这一结果的应用，我们给出了形式幂级数域上代数的洛朗级数的一个间隙定理。我们还将这些结果与洛朗级数场的丢番图性质联系起来。
英文摘要：
This work is devoted to the study of the support of a Laurent series in several variables which is algebraic over the ring of power series over a characteristic zero field. Our first result is the existence of a kind of maximal dual cone of the support of such a Laurent series. As an application of this result we provide a gap theorem for Laurent series which are algebraic over the field of formal power series. We also relate these results to diophantine properties of the fields of Laurent series.
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