Related papers: Weak Greenberg's generalized conjecture for imagin…

Let $k = \mathbb{Q}(\sqrt {-m})$ and $p \geq 3$ split in $k$. We prove new properties of the $\mathbb{Z}_p$-extensions $K/k$, distinct from the cyclotomic one; we do not assume $K/k$ totally ramified, nor the triviality of the $p$-class…

In this paper and a forthcoming joint one with Y. Hachimori we study Iwasawa modules over an infinite Galois extension K of a number field k whose Galois group G=G(K/k) is isomorphic to the semidirect product of two copies of the p-adic…

Let $K$ be an imaginary quadratic field, and fix a prime $p > 3$ that does not divide the class number of $K$. In this paper we prove that Iwasawa's $\lambda$-invariant for the cyclotomic $\mathbb{Z}_p$-extension of $K$ is greater than $1$…

In this paper we establish a connection between the Gauss factorials and Iwasawa's cyclotomic $\lambda$-invariant for an imaginary quadratic field $K$. As a result, we will explain a corespondance between the 1-exceptional primes of…

Let p be an odd prime and let E be an elliptic curve defined over a quadratic imaginary field where p splits completely. Suppose E has supersingular reduction at primes above p. We define and study the fine double-signed residual Selmer…

Our primary goal in this article is to study the Iwasawa theory for semi-ordinary families of automorphic forms on $\mathrm{GL}_2\times\mathrm{Res}_{K/\mathbb{Q}}\mathrm{GL}_1$, where $K$ is an imaginary quadratic field where the prime $p$…

Let k be a totally real number field ant let k$\infty$ be its cyclotomic Zp-extension for a prime p\textgreater{}2. We give (Theorem 3.2) a sufficient condition of nullity of the Iwasawa invariants lambda, mu, when p totally splits in k,…

We formulate integral Iwasawa main conjectures for suitable twists of a newform $f$ that is non-ordinary at $p$, over the cyclotomic $\mathbb{Z}_p$-extension, the anticyclotomic $\mathbb{Z}_p$-extensions (in both the definite and the…

Let l be an odd prime and K/k a Galois extension of totally real number fields with Galois group G such that K/k_\infty and k/Q are finite. We reduce the conjectured triviality of the reduced Whitehead group SK_1(QG) of the algebra…

Kurihara established a refinement of the minus-part of the Iwasawa main conjecture for totally real number fields using the higher Fitting ideals. In this paper, by using Kurihara's methods and Mazur-Rubin theory, we study the higher…

Let $p$ be an odd prime. Consider normalized newforms $f_1,f_2$ that both satisfy the Heegner hypothesis for an imaginary quadratic field $K$ and suppose that they induce isomorphic residual Galois representations. In the work of…

Let $p$ be an odd prime. We study the structure of the cyclotomic Greenberg-Selmer group attached to a general irreducible Artin motive over $\mathbb{Q}$ endowed with an ordinary $p$-stabilization. Under the Leopoldt and the weak $p$-adic…

This paper is about the Iwasawa theory of elliptic curves over the cyclotomic $\mathbb{Z}_p$-extension $\mathbb{Q}^{\text{cyc}}$ of $\mathbb{Q}$. We discuss a deep conjecture of Greenberg that if $E/\mathbb{Q}$ is an elliptic curve with…

We consider a finite, abelian, CM extension $H/F$ of a totally real number field $F$, and construct a $\mathbb{Z}_p[[G(H_\infty/F)]]-$module $\nabla_S^T(H_\infty)_p$, where $p>2$ is a prime and $H_\infty$ is the cyclotomic $\Bbb…

In this paper, we relate three objects. The first is a particular value of a cup product in the cohomology of the Galois group of the maximal unramified outside p extension of a cyclotomic field containing the pth roots of unity. The second…

Let $K$ be an imaginary quadratic field where $p$ is inert. Let $E$ be an elliptic curve defined over $K$ and suppose that $E$ has good supersingular reduction at $p$. In this paper, we prove that the plus/minus Selmer group of $E$ over the…

We prove the Kac-Wakimoto conjecture for the periplectic Lie superalgebra $\mathfrak{p}(n)$, stating that any simple module lying in a block of non-maximal atypicality has superdimension zero.

Let $E/\mathbb{Q}$ an elliptic curve with good supersingular reduction at a prime $p\geq 5$, and $K$ an imaginary quadratic field such that the root number of $E$ over $K$ equals $-1$. When $p$ splits in $K$, Castella and Wan formulated the…

For any positive integer $n$, we show that there exists a real number field $k$ (resp. $k'$) of degree $2^n$ whose $2$-class group is isomorphic $\mathbb{Z}/2\mathbb{Z}\times \mathbb{Z}/2\mathbb{Z}$ such that the Galois group of the maximal…

We study the behavior of the Iwasawa invariants of the Iwasawa modules which appear in Kato's main conjecture without $p$-adic $L$-functions under congruences. It generalizes the work of Greenberg-Vatsal, Emerton-Pollack-Weston, B.D. Kim,…