论文标题
理性函数场的差分Galois组
The differential Galois group of the rational function field
论文作者
论文摘要
我们确定了理性函数的$ \ mathbb {c}（x）$的绝对差分galois组：这是一组基数$ | \ mathbb {c} | $的免费proalgebraic组。这解决了B.H.带来的长期开放问题Matzat。为了证明，我们在分裂嵌入问题方面开发了新的proalgebraic组的新表征，并且我们使用修补技术来解决非常一般的差分嵌入问题类别。我们的结果约为$ \ mathbb {c}（x）$，也适用于更一般的系数字段。
We determine the absolute differential Galois group of the field $\mathbb{C}(x)$ of rational functions: It is the free proalgebraic group on a set of cardinality $|\mathbb{C}|$. This solves a longstanding open problem posed by B.H. Matzat. For the proof we develop a new characterization of free proalgebraic groups in terms of split embedding problems, and we use patching techniques in order to solve a very general class of differential embedding problems. Our result about $\mathbb{C}(x)$ also applies to rational function fields over more general fields of coefficients.
