A VARIATION OF SWEEDLERS COMPLEX AND THE GROUP OF GALOIS OBJECTS OF AN INFINITE HOPF ALGEBRA

Let H be a cocommutative faithfully flat Hopf algebra over a commutati ve ring R. We give a four term exact sequence describing the group of H-Galois objects. This generalizes an exact sequence due to Early and Kreimer and Yokogawa. We have to introduce the Picard group of a coalg ebra, and a new type of Sweedler cohomology. Using methods of Villamay or and Zelinsky and Hattori, we can extend the four term exact sequenc e to a sequence of infinite length.