线性微分代数群的微分Galois上同调的平凡性
Triviality of differential Galois cohomologies of linear differential algebraic groups
摘要：
我们证明了线性微分代数群的偏微分域K上的微分伽罗瓦上同调的平凡性等价于K在代数上、Picard-Vessiot和线性微分闭.这也被称为前者是等价的唯一性，直到同构的Picard-Vessiot扩张的线性微分方程的参数。
英文摘要：
We show that the triviality of the differential Galois cohomologies over a partial differential field K of a linear differential algebraic group is equivalent to K being algebraically, Picard-Vessiot, and linearly differentially closed. This former is also known to be equivalent to the uniqueness up to an isomorphism of a Picard-Vessiot extension of a linear differential equation with parameters.
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