Related papers: Fitting ideals in two-variable equivariant Iwasawa…
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 this paper we prove that the p-adic L-function that interpolates the Rankin-Selberg product of a general modular form and a CM form of higher weight divides the characteristic ideal of the corresponding Selmer group. This is one…
In this article, we study a relation between certain quotients of ideal class groups and the cyclotomic Iwasawa module $X_\infty$ of the Pontrjagin dual of the fine Selmer group of an elliptic curve $E$ defined over $\mathbb{Q}$. We…
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…
In this paper, for a CM abelian extension $K/k$ of number fields, we propose a conjecture which describes completely the Fitting ideal of the minus part of the Pontryagin dual of the $T$-ray class group of $K$ for a set $T$ of primes as a…
A fundamental observation of Iwasawa gives a criterion for a module over the classical Iwasawa algebra to be torsion. In this paper, we study a certain extension of this criterion. We will then apply this to study the structure of the…
In this paper, we study a (p-adic) geometric analogue for abelian varieties over a function field of characteristic p of the cyclotomic Iwasawa theory and the non-commutative Iwasawa theory for abelian varieties over a number field…
In this article we construct characteristic elements for a certain class of Iwasawa modules in noncommutative Iwasawa theory. These elements live in the first K-group K_1(L_T) of the localisation L_T of the Iwasawa algebra L=L(G) of a…
We construct a compatible family of global cohomology classes (an Euler system) for the symmetric square of a modular form, and apply this to bounding Selmer groups of the symmetric square Galois representation and its twists.
This paper explores Iwasawa theory from a graph theoretic perspective, focusing on the algebraic and combinatorial properties of Cayley graphs. Using representation theory, we analyze Iwasawa-theoretic invariants within…
We establish the Iwasawa main conjecture for semi-stable abelian varieties over a function field of characteristic $p$ under certain restrictive assumptions. Namely we consider $p$-torsion free $p$-adic Lie extensions of the base field…
In this paper we give a bound for the Iwasawa lambda invariant of an abelian number field attached to the cyclotomic Z_p-extension of that field. We also give some properties of Iwaswa power series attached to p-adic L-functions.
In this paper we prove that the $p$-adic $L$-function that interpolates the Rankin-Selberg product of a general weight two modular form which is unramified and non-ordinary at $p$, and an ordinary CM form of higher weight contains the…
Iwasawa's classical asymptotical formula relates the orders of the $p$-parts $X_n$ of the ideal class groups along a $\ZM_p$-extension $F_\infty/F$ of a number field $F$, to Iwasawa structural invariants $\la$ and $\mu$ attached to the…
Iwasawa's classical asymptotical formula relates the orders of the $p$-parts $X_n$ of the ideal class groups along a $\ZM_p$-extension $F_\infty/F$ of a number field $F$, to Iwasawa structural invariants $\la$ and $\mu$ attached to the…
In this article, we study the Iwasawa theory for cuspidal automorphic representations of $\mathrm{GL}(n)\times\mathrm{GL}(n+1)$ over CM fields along anticyclotomic directions, in the framework of the Gan--Gross--Prasad conjecture for…
We discuss three different formulations of the equivariant Iwasawa main conjecture attached to an extension K/k of totally real fields with Galois group G, where k is a number field and G is a p-adic Lie group of dimension 1 for an odd…
Let R be a complete discrete valuation ring, S=R[[u]] and n a positive integer. The aim of this paper is to explain how to compute efficiently usual operations such as sum and intersection of sub-S-modules of S^d. As S is not principal, it…
We prove that the Mazur-Tate elements of an eigenform $f$ sit inside the Fitting ideals of the corresponding dual Selmer groups along the cyclotomic $\mathbb Z_p$-extension (up to scaling by a single constant). Our method begins with the…
These expository notes introduce $p$-adic $L$-functions and the foundations of Iwasawa theory. We focus on Kubota--Leopoldt's $p$-adic analogue of the Riemann zeta function, which we describe in three different ways. We first present a…