Abundant central extensions of non-trivial genera

K. Miyake, N. Ormerod
1984 Nagoya mathematical journal  
Letkbe either a local or a global field, andKbe a finite Galois extension ofkwith g = Gal (K/k). Let L be a Galois extension ofKwhich is also Galois overk. Such an extension is called central if Gal(L/iT) lies inside the centre of Gal(L/K). ClearlyLis abelian overK. Next set L* =L∩K · kabwherekabis the maximal abelian extension ofkin its algebraic closure. This is the genus field ofLoverK/k.
doi:10.1017/s002776300002095x fatcat:lp46565ejzhpxmxuqfla2uggfe