Let p be a prime number and k a finite extension of Q. It is conjectured that Iwasawa invariants λp(k) and μp(k) vanish for all p and totally real number fields k. Using cyclotomic units and Gauss sums, we give an effective method for computing the other Iwasawa invariants νp(k) of certain real abelian fields. As numerical examples, we compute Iwasawa invariants associated to k = Q( √ f, ζp + ζ...

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...

Let f be a modular eigenform of weight at least two and let F be a finite abelian extension of Q. Fix an odd prime p at which f is ordinary in the sense that the p Fourier coefficient of f is not divisible by p. In Iwasawa theory, one associates two objects to f over the cyclotomic Zp-extension F∞ of F : a Selmer group Sel(F∞, Af ) (whereAf denotes the divisible version of the two-dimensional G...

We introduce the apollonian metric in Carnot groups using capacity. Extending Beardon’s result for euclidean space, we give an equivalent definition using the cross ratio in Iwasawa groups. We also show that the apollonian metric is bounded above by twice the quasihyperbolic metric in domains in Iwasawa groups.

We consider the computation of the Iwasawa decomposition of a symplectic matrix via the QR factorization. The algorithms presented improve on the method recently described by T.-Y. Tam in [Computing Iwasawa decomposition of a symplectic matrix by Cholesky factorization, Appl. Math. Lett. (in press) doi:10.1016/j.aml.2006.03.001]. c © 2006 Elsevier Ltd. All rights reserved.

Let p be an odd prime. We give an unconditional proof of the equivariant Iwasawa main conjecture for totally real fields for an infinite class of one-dimensional non-abelian p-adic Lie extensions. Crucially, this result does not depend on the vanishing of the relevant Iwasawa μ-invariant.

This paper extends to the pro-$p$ Iwahori subgroup of $GL(2)$ over an unramified finite extension of $mathbb{Q}_p$ the presentation of the Iwasawa algebra obtained earlier by the author for the congruence subgroup of level one of $SL(2‎, ‎mathbb{Z}_p)$‎. ‎It then describes a natural base change map between the Iwasawa algebras or more correctly‎, ‎as it turns out‎, ‎between the global distribut...

let $r$ be an arbitrary ring with identity and $m$ a right $r$-module with $s=$ end$_r(m)$. the module $m$ is called {it rickart} if for any $fin s$, $r_m(f)=se$ for some $e^2=ein s$. we prove that some results of principally projective rings and baer modules can be extended to rickart modules for this general settings.