Field Theory and the Cohomology of Some Galois Groups,

We prove that two arithmetically significant extensions of a field F coincide if and only if the Witt ring WF is a group ring /n[G]. Furthermore, working modulo squares with Galois groups which are 2-groups, we establish a theorem analogous to Hilbertʹs Theorem 90 and show that an identity linking the cohomological dimension of the Galois group of the quadratic closure of F, the length of a filtration on a certain module over a Galois group, and the dimension over 2 of the square class group of the field holds for a number of interesting families of fields. Finally, we discuss the cohomology of a particular Galois group in a topological context.