Partial Fractions and Milnor K-Theory

Abstract

This paper uses partial fraction decompositions to give a direct computation of the logarithmic derivative of the norm in Milnor K-theory for a finite separable extension. This result is useful for computations involving the relative Brauer group in finite characteristic and Witt kernels for function fields in characteristic two. Kato's result that the norm is compatible with the trace under logarithmic differentiation also follows from these tools. When F(x) is rational over F in finite characteristic ℓ, the unramified part of is computed to be .

Key Words:

• Differential forms
• K-Theory

2010 Mathematics Subject Classification:

• Primary: 19D45
• 19E20

ACKNOWLEDGMENT

First author supported by Fondecyt 1090 006 and Proyecto Anillos, PBCT, ACT56.

Second author supported by Proyecto Anillos, PBCT, ACT56.

Notes

Communicated by A. Wadsworth.