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Thoughts on the reduced Whitehead group of the Iwasawa algebra

arXiv:1101.1598

Abstract

Let l be an odd prime and K/k a Galois extension of totally real number fields with Galois group G such that K/k_\infty and k/Q are finite. We reduce the conjectured triviality of the reduced Whitehead group SK_1(QG) of the algebra QG=Quot(ΛG) with the Iwasawa algebra ΛG = Z_l[[G]] to the case of pro-l Galois groups G and finite unramified coefficient extensions.