On the Existence of Unramified Separable Infinite Solvable Extensions of Function Fields over Finite Fields
Hisasi Morikawa · Nagoya Mathematical Journal · 1958
In the present note, using the results in the previous paper, we shall prove the following existence theorem: THEOREM. Let k be a finite field with q elements and K/k be a regular extension of dimension one over k. Then, if q ≧ 11 and the genus gK of K/k is greater than one, there exists an unramified separable infinite solvable extension of K ivhich is regular over k.