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On elementary abelian 2-Sylow K₂ of rings of integers of certain quadratic number fields

P. E. Conner, J. Hurrelbrink (1995)

Acta Arithmetica

A large number of papers have contributed to determining the structure of the tame kernel K F of algebraic number fields F. Recently, for quadratic number fields F whose discriminants have at most three odd prime divisors, 4-rank formulas for K F 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 non-commutative twisting in étale and motivic cohomology

Jens Hornbostel, Guido Kings (2006)

Annales de l’institut Fourier

This article confirms a consequence of the non-abelian Iwasawa main conjecture. It is proved that under a technical condition the étale cohomology groups H 1 ( 𝒪 K [ 1 / S ] , H i ( X ¯ , p ( j ) ) ) , where X Spec 𝒪 K [ 1 / S ] is a smooth, projective scheme, are generated by twists of norm compatible units in a tower of number fields associated to H i ( X ¯ , p ( j ) ) . Using the “Bloch-Kato-conjecture” a similar result is proven for motivic cohomology with finite coefficients.

On the 2-primary part of K₂ of rings of integers in certain quadratic number fields

A. Vazzana (1997)

Acta Arithmetica

1. Introduction. For quadratic fields whose discriminant has few prime divisors, there are explicit formulas for the 4-rank of K E . 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 ( ( p . . . p k ) ) , where the primes p i 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 K E is zero for such fields. In the course of proving...

On the cyclotomic elements in K₂ of a rational function field

Kejian Xu, Chaochao Sun, Shanjie Chi (2014)

Acta Arithmetica

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.

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