Let $E/\mathbf{Q}$ be an elliptic curve of conductor $N$, let $p>3$ a prime where $E$ has good ordinary reduction, and $K$ imaginary quadratic field satisfying the Heegner hypothesis. In 1987, Perrin-Riou formulated Iwasawa main conjecture for Tate-Shafarevich group over anticyclotomic $\mathbf{Z}_p$-extension in terms points. this paper, we give proof Perrin-Riou's under mild hypotheses. Our b...

Let A be the inverse limit of the p-part of the ideal class groups in a Zpextension K∞/K. Greenberg conjectures that if r is maximal, then A is pseudo-null as a module over the Iwasawa algebra Λ (that is, has codimension at least 2). We prove this conjecture in the case that K is the field of p-th roots of unity, p has index of irregularity 1, satisfies Vandiver’s conjecture, and satisfies a mi...

0 Introduction The central point in the Bloch-Kato conjectures is to establish formulas for the order of the Selmer groups attached to Galois representations in terms of the special values of their L-functions. In order to give upper bound, the main way is to construct Euler systems following Kolyvagin. Besides, lower bounds have been obtained by using congruences between automorphic forms. So,...

We study, in the case of ordinary primes, some connections between the GL2 and cyclotomic Iwasawa theory of an elliptic curve without complex multiplication. 2000 Mathematics Subject Classification: 11G05; 11R23.

Poisson-Lie target space duality is a framework where duality transformations are properly defined. In this letter we investigate the dual pair of σ-models defined by the double SO(3,1) in the Iwasawa decomposition .

Refining results of David Burns and Cornelius Greither, respectively Annette Huber and Guido Kings, we formulate and prove an equivariant version of the main conjecture of Iwasawa theory for abelian number fields.

We derive an averaging property under the Iwasawa decomposition on a semisimple Lie group of noncompact type based on a limiting property of random walks in the Lie group.

Recently new results have been obtained in the GL2 Iwasawa theory of elliptic curves without complex multiplication. This article is a survey of some of those results. Mathematics Subject Classification: 11G05, 11R23