Nous associons à chaque corps de nombres un groupe universel analogue au groupe symbolique , et deux sous-groupes canoniques finis et , qui correspondent aux noyaux réguliers et hilbertien de la -théorie, et permettent d’expliciter les correspondances remarquables entre divers modules galoisiens classiques faisant intervenir les conjectures de Leopoldt et de Gross.
A large number of papers have contributed to determining the structure of the tame kernel of algebraic number fields F. Recently, for quadratic number fields F whose discriminants have at most three odd prime divisors, 4-rank formulas for have been made very explicit by Qin Hourong in terms of the indefinite quadratic form x² - 2y² (see [7], [8]). We have made a successful effort, for quadratic number fields F = ℚ (√(±p₁p₂)), to characterize in terms of positive definite binary quadratic forms,...
This article confirms a consequence of the non-abelian Iwasawa main conjecture. It is proved that under a technical condition the étale cohomology groups , where is a smooth, projective scheme, are generated by twists of norm compatible units in a tower of number fields associated to . Using the “Bloch-Kato-conjecture” a similar result is proven for motivic cohomology with finite coefficients.
1. Introduction. For quadratic fields whose discriminant has few prime divisors, there are explicit formulas for the 4-rank of . For quadratic fields whose discriminant has arbitrarily many prime divisors, the formulas are less explicit. In this paper we will study fields of the form , where the primes are all congruent to 1 mod 8. We will prove a theorem conjectured by Conner and Hurrelbrink which examines under what conditions the 4-rank of is zero for such fields. In the course of proving...
If l is a prime number, the cyclotomic elements in the l-torsion of K₂(k(x)), where k(x) is the rational function field over k, are investigated. As a consequence, a conjecture of Browkin is partially confirmed.