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arXiv · 1707.08620

Triviality of differential Galois cohomologies of linear differential algebraic groups

Andrei Minchenko·Alexey Ovchinnikov
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Abstract

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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Andrei Minchenko, Alexey Ovchinnikov. 2017-07-26. Triviality of differential Galois cohomologies of linear differential algebraic groups. https://doi.org/10.1080/00927872.2019.1612416

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