Unramified extensions and geometric ${\mathbb{Z}}_p$-extensions of global function fields

Abstract

We study on finite unramified extensions of global function fields (function fields of one valuable over a finite field). We show two results. One is an extension of Perret's result about the ideal class group problem. Another is a construction of a geometric ${\mathbb{Z}}_p$-extension which has a certain property.

arXiv comment7 pages