An additive variant of Somekawa's K-groups and K?hler differentials

摘要

We introduce a Milnor type K-group associated to commutative algebraic groups over a perfect field. It is an additive variant of Somekawa's Kgroup. We show that the K-group associated to the additive group and q multiplicative groups of a field is isomorphic to the space of absolute K?hler differentials of degree q of the field, thus giving us a geometric interpretation of the space of absolute K?hler differentials. We also show that the K-group associated to the additive group and Jacobian variety of a curve is isomorphic to the homology group of a certain complex.