Scholz admissible moduli of finite Galois extensions of algebraic number fields (Q1428981)

For a finite Galois extension \(K/k\) of algebraic number fields with Galois group \(G\), a modulus \(m\) of \(K\) is called Scholz admissible if the Schur multiplier of \(G\) is isomorphic to the number knot of \(K/k\) modulo \(m\). The present paper develops a systematic treatment for Scholz admissibility. The problem is reduced to the case of a local extension \(K/k\), in particular, the case of a strongly ramified extension. The author studies this local admissibility, whose main object is the \(H^{-1}(G,U^{(s)}_K)\), in detail, and gives a way to estimate for Scholz conductor of \(K/k\) from the ramification in \(K/k\). As an application, an alternative proof of a result of Fröhlich is given.