Tame and wild kernels of quadratic imaginary number fields

Table of Tame and Wild Kernels of Quadratic Imaginary Number Elds of Discriminants > {5000 (conjectural Values)

The 3-adic regulators and wild kernels

For any number field, J.-F. Jaulent introduced a new invariant called the group of logarithmic classes in 1994. This invariant is proved to be closely related to the wild kernels of number fields. In this paper, we show how to compute the kernel of the natural homomorphism from the group of logarithmic classes to the group of p-ideal classes by computing the p-adic regulator which is a classica...

Tame Kernels and Further 4-rank Densities

Abstract. There has been recent progress on computing the 4-rank of the tame kernel K2(OF ) for F a quadratic number field. For certain quadratic number fields, this progress has led to “density results” concerning the 4-rank of tame kernels. These results were first mentioned in [6] and proven in [8]. In this paper, we consider some additional quadratic number fields and obtain further density...

The tame kernel of imaginary quadratic fields with class number 2 or 3

This paper presents improved bounds for the norms of exceptional finite places of the group K2OF , where F is an imaginary quadratic field of class number 2 or 3. As an application we show that K2Z[ √ −10] = 1.

A Note on 4-rank Densities

For certain real quadratic number fields, we prove density results concerning 4-ranks of tame kernels. We also discuss a relationship between 4-ranks of tame kernels and 4-class ranks of narrow ideal class groups. Additionally, we give a product formula for a local Hilbert symbol.