X-unités de certains corps de fonctions algébriques. II. (X-units of some algebraic function fields. II). (French) Zbl 0584.12010

Hellegouarch, Yves

Grupe Étude Théor. Anal. Nombres 1re/2e années: 1984/1985, Exp. No. 19, 14 p. (1985).

Let k(X) be the field of rational functions over the field k, \(A=k[X]\) the polynomial ring, and p a natural number prime to char(k). E denoting the field k(X,Y), where \(Y^ p=D\), D a certain polynomial in A, the author determines
- the unit groups of orders in E with respect to A;
- the integral closure of A in E.

Reviewer: E.-U.Gekeler

MSC:

11R58	Arithmetic theory of algebraic function fields
14H45	Special algebraic curves and curves of low genus
14H40	Jacobians, Prym varieties
11D57	Multiplicative and norm form equations

Keywords:

norm equations; hyperelliptic curves; rational functions; unit groups of orders; integral closure

Citations:

Zbl 0584.12009