Related papers: Higher Fitting ideals and the structure of anticyc…

We give a short proof of the anticyclotomic analogue of the "strong" main conjecture of Kurihara on Fitting ideals of Selmer groups for elliptic curves with good ordinary reduction under mild hypotheses. More precisely, we completely…

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, we study the higher Fitting ideals of the plus-part of the Iwasawa module…

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…

We study equivariant Iwasawa theory for two-variable abelian extensions of an imaginary quadratic field. One of the main goals of this paper is to describe the Fitting ideals of Iwasawa modules using $p$-adic $L$-functions. We also provide…

In this paper, we study the Fitting ideals of Selmer groups over finite subextensions in the cyclotomic $\mathbb{Z}_p$-extension of $\mathbb{Q}$ of an elliptic curve over $\mathbb{Q}$. Especially, we present a proof of the "weak main…

In our previous work, by using Kolyvagin derivatives of elliptic units, we constructed ideals C_i of the Iwasawa algebra, and proved that the ideals C_i become "upper bounds" of the higher Fitting ideals of the one and two variable p-adic…

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…

We reveal a new and refined application of (a weaker statement than) the Iwasawa main conjecture for elliptic curves to the structure of Selmer groups of elliptic curves of arbitrary rank. For a large class of elliptic curves, we obtain the…

We develop the theory of equivariant, ultra Kolyvagin systems to bypass structural limitations of the Euler system machinery over infinite rings. By utilizing collections of classes living in the exterior powers of patched Selmer groups --…

Let $E$ be an elliptic curve defined over $\mathbb{Q}$, and let $K$ be an imaginary quadratic field. Consider an odd prime $p$ at which $E$ has good supersingular reduction with $a_p(E)=0$ and which is inert in $K$. Under the assumption…

Let $p>3$ be a prime number and $K$ be an imaginary quadratic field where $p$ splits. Let $K_\infty$ be the $\mathbf{Z}_p^2$-extension of $K$ and let $K_n$ be a finite subextension of $K_\infty/K$. Let $E$ be an elliptic curve with good…

Under a non-torsion assumption on Heegner points, results of Kolyvagin describe the structure of Shafarevich-Tate groups of elliptic curves. In this paper we prove analogous results for ($p$-primary) Shafarevich-Tate groups associated with…

We establish several results towards the two-variable main conjecture of Iwasawa theory for elliptic curves without complex multiplication over imaginary quadratic fields, namely (i) the existence of an appropriate p-adic L-function,…

In this paper, we use techniques from Iwasawa theory to study questions about rank jump of elliptic curves in cyclic extensions of prime degree. We also study growth of the $p$-primary Selmer group and the Shafarevich--Tate group in cyclic…

Let $E$ be an elliptic curve defined over a number field $K$ where $p$ splits completely. Suppose that $E$ has good reduction at all primes above $p$. Generalizing previous works of Kobayashi and Sprung, we define multiply signed Selmer…

Let $p\ge 5$ be a prime number and $E/\mathbf{Q}$ an elliptic curve with good supersingular reduction at $p$. Under the generalized Heegner hypothesis, we investigate the $p$-primary subgroups of the Tate--Shafarevich groups of $E$ over…

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…

Let $A$ be an abelian variety defined over a global field $F$ of positive characteristic $p$ and let $\calf/F$ be a $\Z_p^{\N}$-extension, unramified outside a finite set of places of $F$. Assuming that all ramified places are totally…

Let $K$ be an imaginary quadratic field and $p$ be an odd prime number. Let $E/\mathbb{Q}$ be an elliptic curve with good ordinary reduction at $p$. We study the Iwasawa theory of $E$ over the anticyclotomic $\mathbb{Z}_p$-extension of $K$…

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…