K_1 of some noncommutative group rings

TY - UNPB

T1 - K_1 of some noncommutative group rings

AU - Kakde, Mahesh

N1 - 16 pages.

PY - 2010/3/19

Y1 - 2010/3/19

N2 - In this article I generalise previous computations (by K. Kato, T. Hara and myself) of K_1 (only up to p-power torsion) of p-adic group rings of finite non-abelian p-groups in terms of p-adic group rings of abelian subquotients of the group. Such computation have applications in non-commutative Iwasawa theory due to a strategy proposed by D. Burns, K. Kato (and a modification by T. Hara) for deducing non-commutative main conjectures from commutative main conjectures and certain congruences between special L-values. However, I do not say anything about Iwasawa theory in this article. The details of applications in Iwasawa theory will be presented in a separate paper.

AB - In this article I generalise previous computations (by K. Kato, T. Hara and myself) of K_1 (only up to p-power torsion) of p-adic group rings of finite non-abelian p-groups in terms of p-adic group rings of abelian subquotients of the group. Such computation have applications in non-commutative Iwasawa theory due to a strategy proposed by D. Burns, K. Kato (and a modification by T. Hara) for deducing non-commutative main conjectures from commutative main conjectures and certain congruences between special L-values. However, I do not say anything about Iwasawa theory in this article. The details of applications in Iwasawa theory will be presented in a separate paper.

M3 - Preprint

BT - K_1 of some noncommutative group rings

ER -