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This paper concerns the arithmetic of certain $p$ -adic families of elliptic modular forms. We relate, using a formula of Rubin, some Iwasawa-theoretic aspects of the three items in the title of this paper. In particular, we examine several conjectures, three of which assert the non-triviality of an Euler system, a $p$ -adic regulator, and the derivative of a $p$ -adic $L$ -function. We investigate sufficient conditions for the first conjecture to hold and show that, under additional assumptions, the first...

Ideal Class Groups in Basic ...p1 x....x...ps-Extensions of Abelian Number Fields.

Eduardo C. Friedmann (1981/1982)

Inventiones mathematicae

Imaginär-quadratische Zahlkörper mit einklassigen Geschlechtern

H. Möller (1976)

Acta Arithmetica

Imaginary quadratic fields whose Iwasawa λ-invariant is equal to 1

Dongho Byeon (2005)

Acta Arithmetica

Indice des unités elliptiques dans les $ℤ_{p}$ -extensions

Hassan Oukhaba (2007)

Bulletin de la Société Mathématique de France

Nous comparons le comportement dans les $ℤ_{p}$ -extensions du nombre de classes d’idéaux avec le comportement de l’indice du groupe des unités elliptiques de Rubin.

Indivisibility of special values of Dedekind zeta functions of real quadratic fields

Dongho Byeon (2003)

Acta Arithmetica

Invariants and coinvariants of semilocal units modulo elliptic units

Stéphane Viguié (2012)

Journal de Théorie des Nombres de Bordeaux

Let $p$ be a prime number, and let $k$ be an imaginary quadratic number field in which $p$ decomposes into two primes $𝔭$ and $\bar{𝔭}$ . Let $k_{\infty}$ be the unique $ℤ_{p}$ -extension of $k$ which is unramified outside of $𝔭$ , and let $K_{\infty}$ be a finite extension of $k_{\infty}$ , abelian over $k$ . Let $𝒰_{\infty} / 𝒞_{\infty}$ be the projective limit of principal semi-local units modulo elliptic units. We prove that the various modules of invariants and coinvariants of $𝒰_{\infty} / 𝒞_{\infty}$ are finite. Our approach uses distributions and the $p$ -adic $L$ -function, as defined in [5].

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Global units and ideal class groups.

Greenberg's conjecture and cyclotomic towers

Greenberg’s conjecture for $ℤ_{p}^{d}$ -extensions

Große Faktoren in der Klassengruppe algebraischer Zahlkörper

Groupe des classes de l'algèbre d'un groupe métacyclique.

Groupes des classes d'idéaux triviaux

Groupes d'unités elliptiques

Hida families, $p$ -adic heights, and derivatives

Ideal Class Groups in Basic ...p1 x....x...ps-Extensions of Abelian Number Fields.

Imaginär-quadratische Zahlkörper mit einklassigen Geschlechtern

Imaginary quadratic fields whose Iwasawa λ-invariant is equal to 1

Indice des unités elliptiques dans les $ℤ_{p}$ -extensions

Indivisibility of special values of Dedekind zeta functions of real quadratic fields

Invariants and coinvariants of semilocal units modulo elliptic units

...-Invariants and ...-Transforms.

Irregular imaginary fields

Iwasawa algebras and arithmetic

Iwasawa Invariants.

Iwasawa Invariants of Abelian Number Fields.

Iwasawa invariants of imaginary quadratic fields.

Currently displaying 161 – 180 of 467