Odd parts of tame kernels of dihedral extensions
On elementary abelian 2-Sylow K₂ of rings of integers of certain quadratic number fields
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,...
On K2 (...) and presentations of SLn (...) in the real quadratic case.
On non-commutative twisting in étale and motivic cohomology
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.
On Sylow 2-subgroups of K2OF for quadratic number fields F.
On the 2-primary part of a conjecture of Birch and Tate
On the 2-primary part of K₂ of rings of integers in certain quadratic number fields
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...
On the 2-Sylow subgroup of the Hilbert kernel of of number fields
On the 4-rank of tame kernels of quadratic number fields
On the cyclotomic elements in K₂ of a rational function field
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.
On the elements of prime power order in K₂ of a number field
On the homology of the special linear group ove a number field.
On the K-Theory of Algebraically Closed Fields.
On the non-torsion elements in the algebraic K-theory of rings of integers.
On the odd part of tame kernels of biquadratic number fields
On the p-rank of the tame kernel of algebraic number fields.
On the real cohomology of arithmetic groups and the rank conjecture for number fields
On two-primary algebraic K-theory of quadratic number rings with focus on K₂