If I work over a field k,write D for the formal disk k[[t]] and D<sup>x</sup> for the formal punctured disk k((t)), then there is an associated long exact sequence in algebraic K-theory

... K<sub>n+1</sub>(D<sup>x</sup>) --> K<sub>n</sub>(k) --> K<sub>n</sub>(D) --> K<sub>n</sub>(D<sup>x</sup>) ...

I want to know, what happens if we replace the base k by a more general scheme?

(I am particularly interested in the map K<sub>2</sub>(D<sup>x</sup>) --> K<sub>1</sub>(k) (which must be the tame symbol right?))