The K-theory of strict Hensel local rings and a theorem of Suslin (Q1065875): Difference between revisions

The main result is a comparison theorem for K-theories: Let R be the strict Henselization of a local ring at a smooth point of a variety of finite type over a separably closed field k. Let \(n\in {\mathbb{Z}}\) be prime to char(k). Then \(K_*(k;{\mathbb{Z}}/n)\to^{\sim}K_*(R;{\mathbb{Z}}/n).\) The authors use this to give a partial confirmation of a conjecture of Quillen and Lichtenbaum in characteristic 0, which previously has been proved by Suslin in the case of positive characteristic.