On geometric \({\mathbb{Z}}_ p\)-extensions of function fields (Q1113949)

In the paper under review the authors give a very nice treatment of the Iwasawa theory of geometric \({\mathbb{Z}}_ p\)-extensions of function fields. The authors examine the rate of growth of the class number in such extensions. They establish that it grows much faster in this situation than in either the cyclotomic situation or the case of constant field extensions. They also show that there is much wider variety of Iwasawa modules that arise in the function field case than in the number field case. Finally, they present some examples of \({\mathbb{Z}}^ 2_ p\)- extensions which have nontrivial invariants in the sense of Monsky and Cuoco.