The Picard-Vessiot theory, constrained cohomology, and linear   differential algebraic groups
  We prove that a differential field K is algebraically closed and Picard-Vessiot closed if and only if the differential Galois cohomology group H^1_\partial(K,G) is trivial for any linear differential algebraic group G over K. We give an application to the parameterized Picard-Vessiot theory. 
Anand Pillay
math.AG