Calculus of absolute Kahler forms and Milnor K-theory

Abstract

We develop a basic calculus for absolute Kahler forms over the formal power series rings of a field of characteristic 0. We show that for the single variable ring, one has a well-defined integral of a form in the relative Milnor K-groups. For the multivariable case, a partial answer is given. Using these, we give the notion of Chen's iterated integrals for the absolute forms, and define the logarithms. The logarithms describe the projections from the Milnor K-groups to the relative Milnor K-groups.