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The Picard-Vessiot theory, constrained cohomology, and linear differential algebraic groups (1610.09548v1)
Published 29 Oct 2016 in math.AG
Abstract: We prove that a differential field K is algebraically closed and Picard-Vessiot closed if and only if the differential Galois cohomology group H1_\partial(K,G) is trivial for any linear differential algebraic group G over K. We give an application to the parameterized Picard-Vessiot theory.