Related papers: Sur la nullit\'e du mu-invariant d'Iwasawa des cor…

We improve an estimate of A.Granville (1987) on the number of vanishing Fermat quotients $q_p(\ell)$ modulo a prime $p$ when $\ell$ runs through primes $\ell \le N$. We use this bound to obtain an unconditional improvement of the…

Let $f$ be a newform of even weight at least $4$, level $N$ and trivial character. Let $p\nmid N$ be an odd prime number that is ordinary for $f$ and let $K$ be an imaginary quadratic field satisfying a generalized Heegner hypothesis…

In this paper, we make a study of the Iwasawa theory of an elliptic curve at a supersingular prime p along an arbitrary Z_p-extension of a number field K in the case when p splits completely in K. Generalizing work of Kobayashi and…

Let $k_\infty$ be the cyclotomic $\mathbb{Z}_p$-extension field of an algebraic number field $k$. Moreover, we take a $\mathbb{Z}_p$-extension $K_\infty$ over $k_\infty$. In this paper, we study the behavior of the $p$-part of the class…

Fix an odd prime $p$. Let $G$ be a compact $p$-adic Lie group containing a closed, normal, pro-$p$ subgroup $H$ which is abelian and such that $G/H$ is isomorphic to the additive group of $p$-adic integers $\mathbbZ_p$ . First we assume…

In this article we study the Iwasawa theory for Hecke characters associated with CM abelian varieties and Hilbert modular forms at ordinary primes. We formulate and prove a result concerning the anticyclotomic Iwasawa main conjecture for CM…

Following Deligne and Ribet (`Values of abelian $L$-functions at negative integers over totally real fields.' Invent. Math. 59 (1980), 227-286) we prove that the `torsion congruences' (as introduced in our paper `Non-abelian pseudomeasures…

Let $K$ be a totally real number field of degree $r=[K:\mathbb{Q}]$ and let $p$ be an odd rational prime. Let $K_{\infty}$ denote the cyclotomic $\mathbb{Z}_{p}$-extension of $K$ and let $L_{\infty}$ be a finite extension of $K_{\infty}$,…

The goal of this article is to obtain a proof of the Main conjectures of Iwasawa theory for rational elliptic curves over anticyclotomic extensions of imaginary quadratic fields, under mild arithmetic assumptions, both in the case where the…

This paper has been withdrawn by the author due to incomplete interpretation for the results.

We study the Selmer group associated to a $p$-ordinary newform $f \in S_{2r}(\Gamma_0(N))$ over the anticyclotomic $\mathbb{Z}_p$-extension of an imaginary quadratic field $K/\mathbb{Q}$. Under certain assumptions, we prove that this Selmer…

In the present paper, we study the $p$-adic $L$-functions and the (strict) Selmer groups over $\mathbb{Q}_{\infty}$, the cyclotomic $\mathbb{Z}_p$-extension of $\mathbb{Q}$, of the $p$-adic weight one cusp forms $f$, obtained via the…

Main theorem of [Buyukboduk, arXiv:0706.0377v1] suggests that it should be possible to lift the Kolyvagin systems of Stark units constructed in [Buyukboduk, arXiv:math/0703426v1] to a Kolyvagin system over the cyclotomic Iwasawa algebra.…

In Part I we review some specific properties of the $\Lambda$-modules in Iwasawa theory, which add structure to the general properties of Noetherian $\Lambda$-torsion modules. Part II deals with Kummer theory and gives a detailed…

For $\Gamma=\mathbb{Z}_p$, Iwasawa was the first to construct $\Gamma$-extensions over number fields with arbitrarily large $\mu$-invariants. In this work, we investigate other uniform pro-$p$ groups which are realizable as Galois groups of…

Let $p\ge 5$ be a prime number, $E/\mathbb{Q}$ an elliptic curve with good supersingular reduction at $p$ and $K$ an imaginary quadratic field such that the root number of $E$ over $K$ is $+1$. When $p$ is split in $K$, Darmon and Iovita…

The Iwasawa theory of CM fields has traditionally concerned Iwasawa modules that are abelian pro-p Galois groups with ramification allowed at a maximal set of primes over p such that the module is torsion. A main conjecture for such an…

Let $A$ be an ordinary elliptic curve over a global function field $K$ of characteristic $p$, assumed semistable at every place, and let $L/K$ be a $\mathbb{Z}_p^d$-extension ramified only at finitely many places where $A$ has ordinary…

This paper has been withdrawn by the author

The Kida's formula in classical Iwasawa theory relates the Iwasawa $\lambda$-invariants of $p$-extensions of number fields. Analogue of this formula was subsequently established for the Iwasawa $\lambda$-invariants of Selmer groups under an…