On the 4-rank of tame kernels of quadratic number fields
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.
For a typical example of a complete discrete valuation field of type II in the sense of [12], we determine the graded quotients for all . In the Appendix, we describe the Milnor -groups of a certain local ring by using differential modules, which are related to the theory of syntomic cohomology.