Wojciech J. Gajda

Abstract:

We present a short introduction to the main features of Iwasawa theory in the function field setting. We focus in particular on class groups for the cyclotomic Z_p^\infty-extension generated by the \p-torsion of the Carlitz module and prove an Iwasawa Main Conjecture relating the Fitting ideal of Iwasawa modules (i.e., class groups in this case) to a \p-adic L-function. As an application we provide an analog of the Ferrero-Washington theorem and some information on the values of the Goss-Carlitz zeta-function at odd negative integers.