Amitsur cohomology of cubic extensions of algebraic integers

LetK be the rational fieldQ or a complex quadratic number field other than\(Q(\sqrt { - 3} )\). LetL be a normal three-dimensional field extension onK. IfR andS are the rings of algebraic integers ofK andL respectively, then the Amitsur cohomology groupH 2 (S/R, U) is trivial. Inflation and class numbers give information about cohomology arising from certain nonnormal cubic extensions.