The Merkuriev–Suslin theorem for any semi-local ring

We introduce here a method which uses étale neighborhoods to extend results from smooth semi-local rings to arbitrary semi-local rings AA by passing to the henselization of a smooth presentation of AA. The technique is used to show that étale cohomology of AA agrees with Galois cohomology, to show that the Merkuriev–Suslin theorem holds for AA, and to describe torsion in K2(A)K2(A).