In this paper we prove that over local or global fields of characteristic 0, the Corestriction Principle holds for kernel and image of all maps which are connecting maps in group cohomology which extends an earlier result due to Deligne and can be considered as cohomological counterpart to a result of Lenstra and Tate.
"On Corestriction Principle in non abelian galois cohomology over local and global fields." J. Math. Kyoto Univ. 42 (2) 287 - 304, 2002. https://doi.org/10.1215/kjm/1250283871