Hilbert 90 for Galois cohomology
  Assuming the Bloch-Kato Conjecture, we determine precise conditions under which Hilbert 90 is valid for Milnor k-theory and Galois cohomology. In particular, Hilbert 90 holds for degree n when the cohomological dimension of the Galois group of the maximal p-extension of F is at most n. 
Nicole Lemire, Jan Minac, Andrew Schultz, John Swallow