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Tame kernels of cyclic extensions of number fields

Haiyan Zhou (2009)

Acta Arithmetica

Tame kernels of quintic cyclic fields

Xia Wu (2008)

Acta Arithmetica

The 2-Sylow subgroups of the tame kernel of imaginary quadratic fields

Hourong Qin (1995)

Acta Arithmetica

1. Introduction. Let F be a number field and $O_{F}$ the ring of its integers. Many results are known about the group $K ₂ O_{F}$ , the tame kernel of F. In particular, many authors have investigated the 2-Sylow subgroup of $K ₂ O_{F}$ . As compared with real quadratic fields, the 2-Sylow subgroups of $K ₂ O_{F}$ for imaginary quadratic fields F are more difficult to deal with. The objective of this paper is to prove a few theorems on the structure of the 2-Sylow subgroups of $K ₂ O_{F}$ for imaginary quadratic fields F. In our Ph.D. thesis (see...

The 3-ranks of tame kernels of cubic cyclic number fields

Xuejun Guo (2007)

Acta Arithmetica

The 4-rank of $K ₂ O_{F}$ for real quadratic fields F

Hourong Qin (1995)

Acta Arithmetica

The 4-rank of the tame kernel versus the 4-rank of the narrow class group in quadratic number fields

Qin Yue, Keqin Feng (2000)

Acta Arithmetica

The 8-rank of tame kernels of quadratic number fields

Xuejun Guo, Hourong Qin (2012)

Acta Arithmetica

The Bloch-Wigner-Ramakrishnan polylogarithm function.

Don Zagier (1990)

Mathematische Annalen

The functor $K_{2}$ for the ring of integers of a number field

Jerzy Browkin (1982)

Banach Center Publications

The Iwasawa invariants and the higher $K$ -groups associated to real quadratic fields.

Sumida-Takahashi, Hiroki (2005)

Experimental Mathematics

The structure of the 2-Sylow-subgroup of K2(...), I.

Manfred Kolster (1986)

Commentarii mathematici Helvetici

The structure of the tame kernels of quadratic number fields (II)

Xiaobin Yin, Hourong Qin, Qunsheng Zhu (2005)

Acta Arithmetica

The structure of the tame kernels of quadratic number fields (I)

H. R. Qin (2004)

Acta Arithmetica

The Sylow p-Subgroups of Tame Kernels in Dihedral Extensions of Number Fields

Qianqian Cui, Haiyan Zhou (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

Let F/E be a Galois extension of number fields with Galois group $D_{2 ⁿ}$ . In this paper, we give some expressions for the order of the Sylow p-subgroups of tame kernels of F and some of its subfields containing E, where p is an odd prime. As applications, we give some results about the order of the Sylow p-subgroups when F/E is a Galois extension of number fields with Galois group $D_{16}$ .

Théorèmes de réflexion

Georges Gras (1998)

Journal de théorie des nombres de Bordeaux

Soit $K$ un corps de nombres contenant $μ_{p}$ et muni d’un groupe d’automorphismes $G$ d’ordre étranger à $p$ ; pour toute représentation $𝔽_{p}$ -irréductible $V_{χ}$ de $G$ , de caractère $χ$ , et tout $G$ -module $M$ , soit rg $_{χ} (M)$ l’entier $r$ maximum tel que $M / M^{p}$ contienne $V_{χ}^{r}$ . Nous établissons par exemple la formule générale explicite suivante : $r g_{χ^{*}} (C ℓ_{T}^{S}) - r g_{χ} (C ℓ_{S}^{T}) = ρ_{χ} (T, S),$ où $T$ et $S$ sont des ensembles finis disjoints de places de $K$ tels que $T \cup S$ contienne les places au-dessus de $p \infty$ , où $C ℓ_{T}^{S}$ est le groupe de classes généralisées qui correspond, par le corps de classes, au...

Total positivity and algebraic Witt classes.

D.R. Estes, J. Hurrelbrink, R. Perlis (1985)

Commentarii mathematici Helvetici

Trace maps in algebraic K-theory and the Coates-Wiles homomorphism.

I. Madsen, S. Bentzen (1990)

Journal für die reine und angewandte Mathematik

Trivialité du $2$ -rang du noyau hilbertien

Hervé Thomas (1994)

Journal de théorie des nombres de Bordeaux

We give exhaustive list of biquadratic fields $K = ℚ (i, \sqrt{m})$ and $K = ℚ (\sqrt{2}, \sqrt{m})$ without $2$ -exotic symbol, i.e. for which the $2$ -rank of the Hilbert kernel (or wild kernel) is zero. Such $K = ℚ (i, \sqrt{m})$ are logarithmic principals [J3]. We detail an exemple of this technical numerical exploration and quote the family of theories and results we utilize. The $2$ -rank of tame, regular and wild kernel of $K$ -theory are connected with local and global problem of embedding in a $Z_{2}$ -extension. Global class field theory can describe the $2$ -rank of the Hilbert...

Wild kernels at the prime 2

Paul Arne Østvær (2004)

Acta Arithmetica

Zagier’s conjecture and Wedge complexes in algebraic $K$ -theory

Rob de Jeu (1995)

Compositio Mathematica

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