The finiteness of NK1(Z[G])

作者：Grunewald Joachim^*

来源：Forum Mathematicum, 2010, 22(2): 269-275.

DOI：10.1515/FORUM.2010.15

For a finite group G it was known that the abelian group NK0(ZG) is always finitely generated over the Verschiebung algebra. This result inspired Connolly and the author to asked the question whether NK1(ZG) is also finitely generated over the Verschiebung algebra. Based on a computation of Weibel we obtain a negative answer to this question by proving that NK1(Z[C(2)xC(2)]) is not finitely generated over the larger Verschiebung and Frobenius algebra.
This raises the question of a different finiteness of NK1. In the last part we show that the filtration on NK1(ZG) which is induced by the degree of a polynomial has the property that the quotients are finite groups.

• 出版日期2010-3