On Tamely Ramified Iwasawa Modules for $\Zp$-extensions of Imaginary Quadratic Fields

Zp-Extensions of Imaginary Quadratic Fields

Iwasawa Theory of Zp-Extensions over Global Function Fields

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...

On Small Iwasawa Invariants and Imaginary Quadratic Fields

If p is an odd prime that does not divide the class number of the imaginary quadratic field k , and the cyclotomic Z -extension of k has A-invariant less than or equal to two, we prove that every totally ramified Z extension of k has //-invariant equal to zero and A-invariant less than or equal to two. Combined with a result of Bloom and Gerth, this has the consequence that ß = 0 for every Z -e...

Galois groups of tamely ramified p - extensions par Nigel BOSTON

Very little is known regarding the Galois group of the maximal p-extension unramified outside a finite set of primes S of a number field in the case that the primes above p are not in S. We describe methods to compute this group when it is finite and conjectural properties of it when it is infinite.

Decomposition types in minimally tamely ramified extensions of