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$S$ -classes infinitésimales d’un corps de nombres algébriques

Jean-François Jaulent (1984)

Annales de l'institut Fourier

Nous introduisons les notions de nombres et d’idéaux infinitésimaux attachés à un corps de nombres algébriques $K$ relativement à un nombre premier donné $ℓ$ , et nous interprétons le groupe de Galois $𝒜 (K)$ de la $ℓ$ -extension abélienne $ℓ$ -ramifiée maximale de $K$ comme quotient du tensorisé $Z_{ℓ} \otimes_{Z} J (K)$ du groupe des idéaux étrangers à $ℓ$ par le sous-module engendré par les idéaux principaux-infinitésimaux. Nous en déduisons diverses conséquences sur l’arithmétique des groupes $𝒜 (K)$ , en montrant en particulier qu’ils donnent...

Separable adel algebras and a presentation of Weil groups.

Wolfram Jehne (1987)

Journal für die reine und angewandte Mathematik

Signatures of units and congruences (mod 4) in certain totally real fields.

J.C. Lagarias (1980)

Journal für die reine und angewandte Mathematik

Singular Moduli, Modular Polynomials, and the Index of the Closure of Z [j (...)] in Q (j(...)).

David R. Dorman (1989)

Mathematische Annalen

Solution of a generalised version of a problem of Rankin on sums of powers of cusp-form coefficients

R. W. K. Odoni (2002)

Acta Arithmetica

Some Examples of Weber-Hecke Ring Class Field Theory.

Harvey Cohn (1983)

Mathematische Annalen

Some Invariants of Zd-p-Extensions.

Paul Monsky (1981)

Mathematische Annalen

Some remarks about the power residue symbol

(1994)

Acta Arithmetica

Some remarks on the local class field theory of Serre and Hazewinkel

Takashi Suzuki (2013)

Bulletin de la Société Mathématique de France

We give a new approach for the local class field theory of Serre and Hazewinkel. We also discuss two-dimensional local class field theory in this framework.

Some unramified abelian extensions of algebraic number fields.

Makoto Ishida (1974)

Journal für die reine und angewandte Mathematik

Stark's conjecture in multi-quadratic extensions, revisited

David S. Dummit, Jonathan W. Sands, Brett Tangedal (2003)

Journal de théorie des nombres de Bordeaux

Stark’s conjectures connect special units in number fields with special values of $L$ -functions attached to these fields. We consider the fundamental equality of Stark’s refined conjecture for the case of an abelian Galois group, and prove it when this group has exponent $2$ . For biquadratic extensions and most others, we prove more, establishing the conjecture in full.

Steinitz classes and discriminant counting

Ebru Bekyel (2005)

Acta Arithmetica

Steinitz classes of some abelian and nonabelian extensions of even degree

Alessandro Cobbe (2010)

Journal de Théorie des Nombres de Bordeaux

The Steinitz class of a number field extension $K / k$ is an ideal class in the ring of integers $𝒪_{k}$ of $k$ , which, together with the degree $[K : k]$ of the extension determines the $𝒪_{k}$ -module structure of $𝒪_{K}$ . We denote by $R_{t} (k, G)$ the set of classes which are Steinitz classes of a tamely ramified $G$ -extension of $k$ . We will say that those classes are realizable for the group $G$ ; it is conjectured that the set of realizable classes is always a group.In this paper we will develop some of the ideas contained in [7] to obtain some...

Steinitz classes of tamely ramified nonabelian extensions of odd prime power order

Alessandro Cobbe (2011)

Acta Arithmetica

Stickelberger’s congruences for absolute norms of relative discriminants

Georges Gras (2010)

Journal de Théorie des Nombres de Bordeaux

We give an improvement of a result of J. Martinet on Stickelberger $^{'}$ s congruences for the absolute norms of relative discriminants of number fields, by using classical arguments of class field theory.

Currently displaying 1 – 20 of 37

Page 1 Next

Displaying 1 – 20 of 37

$S$ -classes infinitésimales d’un corps de nombres algébriques

Separable adel algebras and a presentation of Weil groups.

Signatures of units and congruences (mod 4) in certain totally real fields.

Singular Moduli, Modular Polynomials, and the Index of the Closure of Z [j (...)] in Q (j(...)).

Solution of a generalised version of a problem of Rankin on sums of powers of cusp-form coefficients

Some Examples of Weber-Hecke Ring Class Field Theory.

Some Invariants of Zd-p-Extensions.

Some remarks about the power residue symbol

Some remarks on the local class field theory of Serre and Hazewinkel

Some unramified abelian extensions of algebraic number fields.

Stark's conjecture in multi-quadratic extensions, revisited

Steinitz classes and discriminant counting

Steinitz classes of some abelian and nonabelian extensions of even degree

Steinitz classes of tamely ramified nonabelian extensions of odd prime power order

Stickelberger’s congruences for absolute norms of relative discriminants

Strahlknoten und Geschlechterkörper mod m.

Structure galoisienne et corps de classes de rayon de conducteur 2

Superprimes and a generalized Frobenius symbol

Sur la construction d'un corps de Hilbert.

Sur la formule du produit pour le symbole de reste normique généralisé

Currently displaying 1 – 20 of 37