In this paper we study the Iwasawa theory of Zp-extensions of global function fields k over finite fields of characteristic p. When d = 1 we first show that Iwasawa invariants are well defined under the assumption that only finitely many primes are ramified in the extension, then we prove that the Iwasawa μ-invariant can be arbitrarily large for some extension of any given base field k. After g...

The Iwasawa theory of CM fields has traditionally concerned modules that are abelian pro-p Galois groups with ramification allowed at a maximal set primes over p such the module is torsion. A main conjecture for an describes its codimension one support in terms p-adic L-function attached to ramification. In this paper, we study more general and potentially much smaller quotients exterior powers...

This is an introduction to Iwasawa theory and its generalizations. We discuss some main conjectures and related subjects. Mathematics Subject Classification (2000). Primary 11R23; Secondary 11G40, 14G10.

We give a self-contained proof of local class field theory, via Lubin-Tate theory and the Hasse-Arf theorem, refining the arguments of Iwasawa [4].