On the 4-rank of the tame kernel \(K_2(\mathcal O)\) in positive definite terms

DOI10.1006/jnth.2000.2626zbMath0985.11059OpenAlexW2088272510MaRDI QIDQ5935872

P. E. Conner, Juergen Hurrelbrink

Publication date: 1 July 2001

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.2000.2626

zbMATH Keywords

4-rankquadratic number fieldtame kernel

Mathematics Subject Classification ID

(K)-theory of global fields (11R70) Symbols and arithmetic ((K)-theoretic aspects) (19F15)

Related Items (12)

The Structure of the Tame Kernels of Quadratic Number Fields (III) ⋮ A Note on the 4-Rank Densities ofK₂O_Ffor Quadratic Number FieldsF ⋮ Tame kernels of cubic cyclic fields ⋮ 8-ranks of class groups of quadratic number fields and their densities ⋮ The formula of 8-ranks of tame kernels ⋮ Tame kernels for biquadratic number fields ⋮ ANOTHER CASE OF A SCHOLZ'S THEOREM ON CLASS GROUPS ⋮ Quadratic extensions of number fields with elementary abelian 2-prim \(K_2(O_F)\) of smallest rank ⋮ 8-ranks of \(K_2\) of rings of integers in quadratic number fields ⋮ On 2-Sylow Subgroups of Tame Kernels ⋮ On tame kernel and class group in terms of quadratic forms. ⋮ Tame kernels and further 4-rank densities.

Cites Work

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• Relations between \(K_2\) and Galois cohomology
• 8-ranks of \(K_2\) of rings of integers in quadratic number fields
• The 2-Sylow-Subgroup of the Tame Kernel of Number Fields
• The 4-Rank of K₂(0)
• On Sylow 2-subgroups of K2OF for quadratic number fields F.
• Tame and wild kernels of quadratic imaginary number fields
• Elementary abelian 2-primary parts of K₂
• Tame kernels under relative quadratic extensions and Hilbert symbols
• The 2-Sylow subgroups of the tame kernel of imaginary quadratic fields
• The 4-rank of $K₂O_F$ for real quadratic fields F
• On elementary abelian 2-Sylow K₂ of rings of integers of certain quadratic number fields
• On the 2-primary part of K₂ of rings of integers in certain quadratic number fields
• Note on primes of type x2 + 32y2, class number, and residuacity.

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