Zur Arithmetik der zyklischen \(p\)-Körper. (German) Zbl 0016.05205

Schmid, Hermann Ludwig

J. Reine Angew. Math. 176, 161-167 (1936).

Let \(k\) be a perfect field of characteristic \(p\), \(\mathbf K\) be an algebraic extension of finite degree over a simple transcendental extension of \(k\). Then H. Hasse has developed the arithmetic theory of cyclic fields \(\mathbf Z\) of degree \(p\) over \(\mathbf K\) [“Theorie der relativ-zyklischen algebraischen Funktionenkörper usw.”, J. Reine Angew. Math. 172, 37–54 (1934; Zbl 0010.00501)]. The author uses the new vector symbolism of E. Witt and generalizes Hasse’s results to the case of cyclic fields of degree \(p^n\) over \(\mathbf K\). He also determines which ramification points are Weierstrass points.

Reviewer: A. A. Albert (Chicago)

MSC:

11R20

Other abelian and metabelian extensions

Keywords:

cyclic p-fields

Citations:

Zbl 0010.00501