M. Kuenzer and H. Weber

Some additive Galois cohomology rings

Abstract.
Let p > 2 be a prime. We consider the cyclotomic extension
Z_(p)[zeta_{p^2}] over Z_(p), with galois group
G = (Z/p^2)^*. Since this extension is wildly ramified,
the Z_(p)G-module Z_(p)[zeta_{p^2}] is not
projective. We calculate its cohomology ring
H^*(G,Z_(p)[zeta_{p^2}];Z_(p)).
Proceeding in a somewhat greater generality, our results
also apply to certain Lubin-Tate extensions.