On the map between homology of henselization and completion of some local rings Original Research Article

In this note we prove that the integral homology of the special linear group of the henselization of some local rings imbeds into the homology of the special linear group of the completion. We define henselian adele ring and prove that the integral homology of its special linear group injects into the homology of Sl of the finite adele ring. The method of the proof is based on an application of the Artin approximation theorem to the bar complex which calculates the homology.