Pareigis, Bodo; Rosenberg, A.
Addendum to "Amitsur's complex for purely inseparable fields".
In: Osaka Journal of Mathematics, Vol. 1: S. 33-44
We begin this note by pointing out that a few modifications in some
of the notations and arguments of C131 will make these fit in more
closely with results in the literature. We also complete the results of C131
in several points. In particular we point out that the spectral sequence
used in C131 is not quite a genuine generalization of the Hochschild-Serre
spectral sequence in Galois cohomology. However with a slightly different
spectral sequence the results of C131 can also be obtained and we shall
show in section 2 that this is indeed a genuine generalization of the
Hochschild-Serre sequence for Galois cohomology. In section 3 we shall
use some of the results of  to derive an exact sequence complementary
to that of Proposition 7.8 of  from which we deduce the
following result first pointed out to us by S. Shatz: Let C be a field,
C, its separable algebraic closure and its algebraic closure. Then if
X is the lift map [2, Def. 2. 3.1, we have that X : Hr(C,/C)- . ~ ' ( 6 1is~ )
an isomorphism for r = 1,2, ...