Capitulation problem for global function fields

Research paper by Yan Li, Su Hu

Indexed on: 15 Nov '11Published on: 15 Nov '11Published in: Archiv der Mathematik


Let q be a power of an odd prime number \({p, k=\mathbb{F}_{q}(t)}\) be the rational function field over the finite field \({\mathbb{F}_{q}.}\) In this paper, we construct infinitely many real (resp. imaginary) quadratic extensions K over k whose ideal class group capitulates in a proper subfield of the Hilbert class field of K. The proof of the infinity of such fields K relies on an estimation of certain character sum over finite fields.