Related papers: Fine Selmer groups of modular forms

Let $p$ be a prime number. We investigate a refined version of the Iwasawa main conjectures for rational elliptic curves (and more general Galois representations) over anticyclotomic $\mathbb Z_p$-extensions of imaginary quadratic fields,…

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 $K_{\infty}$,…

There is a known analogy between growth questions for class groups and for Selmer groups. If $p$ is a prime, then the $p$-torsion of the ideal class group grows unboundedly in $\mathbb{Z}/p\mathbb{Z}$-extensions of a fixed number field $K$,…

Let f be a cuspidal newform with complex multiplication (CM) and let p be an odd prime at which f is non-ordinary. We construct admissible p-adic L-functions for the symmetric powers of f, thus verifying general conjectures of Dabrowski and…

Given a $p$-adic field $K$ and a nilpotent uniform pro-$p$ group $G$, we prove that all primitive ideals in the $K$-rational Iwasawa algebra $KG$ are maximal, and can be reduced to a particular standard form. Setting $\mathcal{L}$ as the…

In this paper we study when two congruent $l$-adic Galois representations have congruent Selmer groups. We obtain results for representations from cyclotomic characters, Hecke characters and adjoints of modular forms.

Let $\Pi$ be a cuspidal automorphic representation of $\mathrm{GL}_{2n}(\mathbb{A_Q})$ and let $p$ be an odd prime at which $\Pi$ is unramified. In a recent work, Barrera, Dimitrov and Williams constructed possibly unbounded $p$-adic…

Let $K$ be a number field, $A/K$ be an absolutely simple abelian variety of CM type, and $\ell$ be a prime number. We give explicit bounds on the degree over $K$ of the division fields $K(A[\ell^n])$, and when $A$ is an elliptic curve we…

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…

The theory of factor-equivalence of integral lattices establishes a far-reaching relationship between the Galois module structure of the unit group of the ring of integers of a number field and its arithmetic. For a number field $K$ that is…

The notion of the truncated Euler characteristic for Iwasawa modules is a generalization of the the usual Euler characteristic to the case when the cohomology groups are not finite. Let $p$ be an odd prime, $E_1$ and $E_2$ be elliptic…

We prove a slight generalization of Iwasawa's `Riemann-Hurwitz' formula for number fields and use it to generalize Ferrero's and Kida's well-known computations of Iwasawa \lambda-invariants for the cyclotomic Z_2-extensions of imaginary…

For a number field $k$ and an odd prime number $p$, we consider the maximal multiple $\mathbb{Z}_p$-extension $\tilde{k}$ of $k$ and the unramified Iwasawa module $X(\tilde{k})$, which is the Galois group of the maximal unramified abelian…

Let $p >= 5$ be a prime and $E$ an elliptic curve without complex multiplication and let $K_\infty=Q(E[p^\infty])$ be a pro-$p$ Galois extension over a number field $K$. We consider $X(E/K_\infty)$, the Pontryagin dual of the $p$-Selmer…

We generalise works of Kobayashi to give a formulation of the Iwasawa main conjecture for modular forms at supersingular primes. In particular, we give analogous definitions of even and odd Coleman maps for normalised new forms of arbitrary…

The goal of this paper is to illustrate different approaches to understand Euler characteristics in the setting of totally real commutative and non-commutative Iwasawa theory. In addition to this, and in the spirit of Hesselholt and…

Let $p$ be an odd prime and $F_{\infty,\infty}$ a $p$-adic Lie extension of a number field $F$ with Galois group isomorphic to $\mathbb{Z}_p^r\rtimes\mathbb{Z}_p$, $r\geq 1$. Under certain assumptions, we prove an asymptotic formula for 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 give a full description of the algebraic structure of the semisimple algebra QG=Quot(\Lambda G)…

We introduce a new graph invariant of finite groups that provides a complete characterization of the splitting types of unramified prime ideals in normal number field extensions entirely in terms of the Galois group. In particular, each…

Let $A$ be an abelian variety defined over a number field $F$ with supersingular reduction at all primes of $F$ above $p$. We establish an equivalence between the weak Leopoldt conjecture and the expected value of the corank of the…