O devátém Hilbertově problému
O jedenáctém a dvanáctém Hilbertově problému
O rozšíření pojmu kongruence
Obstructions aux déformations de représentations galoisiennes réductibles et groupes de classes
Nous développons une nouvelle stratégie pour comprendre la nature des obstructions aux déformations d’une représentation galoisienne globale réductible, impaire de dimension 2. Ces obstructions s’interprètent en termes de groupe de Šafarevič. D’après [BöMé], elles sont reliées à des conjecture arithmétiques classiques (Conjecture de Vandiver, conjecture de Greenberg). Dans cet article, nous introduisons un autre groupe de Šafarevič associé au corps fixe par . Nous comparons les deux groupes...
Odd parts of tame kernels of dihedral extensions
Okutsu invariants and Newton polygons
On -class field towers of imaginary quadratic number fields
For a number field , let denote its Hilbert -class field, and put . We will determine all imaginary quadratic number fields such that is abelian or metacyclic, and we will give in terms of generators and relations.
On 2-Adic L-Functions and Cyclotomic Invariants.
On 2-extensions of the rationals with restricted ramification
For a finite group G let 𝒦₂(G) denote the set of normal number fields (within ℂ) with Galois group G which are 2-ramified, that is, unramified outside {2,∞}. We describe the 2-groups G for which 𝒦₂(G) ≠ ∅, and determine the fields in 𝒦₂(G) for certain distinguished 2-groups G appearing (dihedral, semidihedral, modular and semimodular groups). Our approach is based on Fröhlich's theory of central field extensions, and makes use of ring class field constructions (complex multiplication).
On 2-rank of the ideal class groups of algebraic number fields.
On 3-class groups of non-Galois cubic fields
On 3-class groups of pure cubic fields.
On a certain additive function on the Gaussian integers
On a Certain l-Adic Representation.
On a certain subideal of the Stickelberger ideal of a cyclotomic field
On A Combinatorial Problem Connected withFactorizations
On a comparison of Gauss sums with products of Lagrange resolvents
On a congruence relation between Jacobi sums and cyclotomic units.
On a conjecture concerning minus parts in the style of Gross
On a conjecture of A. Schinzel and H. Zassenhaus