Milnor–Witt K-groups of local rings

Abstract

We introduce Milnor–Witt K-groups of local rings and show that the nth Milnor–Witt K-group of a local ring R which contains an infinite field of characteristic not 2 is the pull-back of the nth power of the fundamental ideal in the Witt ring of R and the nth Milnor K-group of R over the nth Milnor K-group of R modulo 2. This generalizes the work of Morel–Hopkins on Milnor–Witt K-groups of a field.