A splitting for K-1 of completed group rings

作者：Schneider Peter^*; Venjakob Otmar

来源：Commentarii Mathematici Helvetici, 2013, 88(3): 613-642.

DOI：10.4171/CMH/298

• Completed group ring
• Iwasawa algebra
• algebraic K-group
• Adams operator
• norm operator
• Coleman isomorphism

For p not equal 2 and a uniform pro-p group G and its Iwasawa algebras A (G) := Z(p) [[G]] and Omega[[G]] := Fp [[G]] we show that the natural map K-1(A(G))-%26gt; K-1(Omega(G)) has a splitting provided that SK1(A(G)) vanishes. The image of this splitting is described in terms of a generalised norm operator. This result generalises classical work of Coleman for the case G = Z(p). We verify the vanishing condition for certain unipotent compact p-adic Lie groups.

• 出版日期2013