Triviality of differential Galois cohomology of linear differential algebraic groups.

For a partial differential field , we show that the triviality of the first differential Galois cohomology of every linear differential algebraic group over is equivalent to being algebraically, Picard-Vessiot, and linearly differentially closed. This cohomological triviality condition 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.