On the scope of validity of the norm limitation theorem for quasilocal fields

Original · EN

Let E be a quasilocal field, R/E a finite separable extension, and R ab the maximal abelian subextension of E in R. The main result of this paper shows that the norm groups N(R/E) and N(R ab/E) are equal, if the natural Brauer group homomorphism Br(E) → Br(L) is surjective, for every finite extension L of E. The paper proves in a strong form that the surjectivity of the homomorphisms Br(E) → Br(L) is essential.