Iwasawa Theory of Zp-Extensions over Global Function Fields
نویسندگان
چکیده
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 giving some general results of Zp-extensions we finally study the behaviors of Iwasawa invariants in Zp-extensions in some detail, especially when the extensions contain a constant Zp-extension. The whole paper is expository in nature though it contains some new results.
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