微分代数群的不可分解性
Indecomposability for differential algebraic groups
摘要：
本文研究了微分代数群的不可分解性，它是受模型论和微分代数的启发而提出的。在建立了一些基本的定义和结果之后，我们证明了微分代数群的一个不可分解定理。该定理建立了由无限子簇族生成的微分代数群的子群是微分代数子群的充分判据。这个定理用于各种可定义性结果。例如，我们证明了每一个非交换的几乎单微分代数群是完美的，解决了卡西迪和辛格的问题。我们还建立了许多界限Kolchin多项式，其中一些似乎是以前没有考虑在微分代数几何的性质，特别是，我们建立界限Kolchin多项式的发电机的微分领域的定义微分代数品种。
英文摘要：
We study a notion of indecomposability in differential algebraic groups which is inspired by both model theory and differential algebra. After establishing some basic definitions and results, we prove an indecomposability theorem for differential algebraic groups. The theorem establishes a sufficient criterion for the subgroup of a differential algebraic group generated by an infinite family of subvarieties to be a differential algebraic subgroup. This theorem is used for various definability results. For instance, we show every noncommutative almost simple differential algebraic group is perfect, solving a problem of Cassidy and Singer. We also establish numerous bounds on Kolchin polynomials, some of which seem to be of a nature not previously considered in differential algebraic geometry; in particular, we establish bounds on the Kolchin polynomial of the generators of the differential field of definition of a differential algebraic variety.
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