An additive variant of Somekawa's $K$-groups and K\"ahler differentials
K-Theory and Homology
2014-03-11 v3
Abstract
We introduce a Milnor type -group associated to commutative algebraic groups over a perfect field. It is an additive variant of Somekawa's -group. We show that the -group associated to the additive group and multiplicative groups of a field is isomorphic to the space of absolute K\"ahler differentials of degree of the field, thus giving us a geometric interpretation of the space of absolute K\"ahler differentials. We also show that the -group associated to the additive group and Jacobian variety of a curve is isomorphic to the homology group of a certain complex.
Keywords
Cite
@article{arxiv.1208.6455,
title = {An additive variant of Somekawa's $K$-groups and K\"ahler differentials},
author = {Toshiro Hiranouchi},
journal= {arXiv preprint arXiv:1208.6455},
year = {2014}
}