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

Published online by Cambridge University Press:  20 March 2014

Toshiro Hiranouchi
Toshiro Hiranouchi*
Affiliation:
Department of Mathematics, Graduate School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, 739-8526, Japan, hira@hiroshima–u.ac.jp
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Abstract

We introduce a Milnor type K-group associated to commutative algebraic groups over a perfect field. It is an additive variant of Somekawa's K-group. 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 Kähler differentials of degree q of the field, thus giving us a geometric interpretation of the space of absolute Kähler 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.

Keywords

Milnor K-theoryChow groupsKähler differentials19D4514C15

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Type
Research Article
Information
Journal of K-Theory , Volume 13 , Issue 3 , June 2014 , pp. 481 - 516
Copyright
Copyright © ISOPP 2014 

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