Tame and wild kernels of quadratic imaginary number fields

DOI10.1090/S0025-5718-99-01000-5zbMath0919.11079MaRDI QIDQ4221979

Jerzy Browkin, Herbert Gangl

Publication date: 3 December 1998

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

imaginary quadratic fieldswild kerneltame kernelMilnor \(K\)-groupLichtenbaum conjecture

Mathematics Subject Classification ID

Quadratic extensions (11R11) Algebraic number theory computations (11Y40) (K)-theory of global fields (11R70) Étale cohomology, higher regulators, zeta and (L)-functions ((K)-theoretic aspects) (19F27) Steinberg groups and (K_2) (19C99)

Related Items (22)

On tame and wild kernels of special number fields ⋮ The 3-adic regulators and wild kernels ⋮ Computing the Tame Kernel of ℚ(ζ₈) ⋮ On the tame kernels of imaginary cyclic quartic fields with class number one ⋮ The tame kernel of imaginary quadratic fields with class number 2 or 3 ⋮ On the 2-primary part of tame kernels of real quadratic fields ⋮ On the growth of even \(K\)-groups of rings of integers in \(p\)-adic Lie extensions ⋮ The Structure of the Tame Kernels of Quadratic Number Fields (III) ⋮ Tame kernels of non-abelian Galois extensions of number fields of degree \(q^3\) ⋮ On the \(p\)-rank of tame kernel of number fields ⋮ Reflection Theorems and the Tame Kernel of a Number Field ⋮ On the 4-rank of the tame kernel \(K_2(\mathcal O)\) in positive definite terms ⋮ Reflection theorems and the \(p\)-Sylow subgroup of \(K_{2}O_F\) for a number field \(F\) ⋮ The tame kernel of $\mathbb {Q}(\zeta _{5})$ is trivial ⋮ The shortest vector problem and tame kernels of cyclotomic fields ⋮ The Tame Kernel of Multiquadratic Number Fields ⋮ Hyperbolic tessellations and generators of for imaginary quadratic fields ⋮ Algorithmic approach to logarithmic class groups ⋮ Computing the tame kernel of quadratic imaginary fields ⋮ On the splitting of the exact sequence, relating the wild and tame kernels ⋮ Higher class numbers in extensions of number fields ⋮ Computation of \(K_ 2\) for the ring of integers of quadratic imaginary fields.

Cites Work

• Class fields of abelian extensions of \(\mathbb Q\)
• Generalization of Thue's theorem and computation of the group \(K_ 2 O_ F\)
• Computation of \(K_ 2\mathbb{Z}[\sqrt {-6}\)]
• Twisted \(S\)-units, \(p\)-adic class number formulas, and the Lichtenbaum conjectures
• Computation of \(K_ 2\mathbb{Z}[\frac{1+\sqrt{-35}}{2}\)]
• On Sylow 2-subgroups of K2OF for quadratic number fields F.
• On the p-rank of the tame kernel of algebraic number fields.
• The 2-Sylow subgroups of the tame kernel of imaginary quadratic fields
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