论文标题
安德烈解决方案代数的一般理论
A general theory of André's solution algebras
论文作者
论文摘要
我们将伊夫·安德烈（YvesAndré）的解决方案代数理论扩展到了坦纳基（Tannakian）的一般环境。作为应用，我们在Galois组的溶液场和可观察到的亚组之间建立了他的对应关系的类似物，用于在正特征和差异方程中的迭代微分方程。在差异代数环境中，解决方案代数的使用还为超越理论中的菲利普和adamczewski-faverjon的最新结果做出了新的方法。
We extend Yves André's theory of solution algebras in differential Galois theory to a general Tannakian context. As applications, we establish analogues of his correspondence between solution fields and observable subgroups of the Galois group for iterated differential equations in positive characteristic and for difference equations. The use of solution algebras in the difference algebraic context also allows a new approach to recent results of Philippon and Adamczewski--Faverjon in transcendence theory.
