### A cohomological approach to properties of the norm residue symbol in higher dimensional class field theory, by Robert A. Bell

In earlier work the author proved that the Vostokov symbol
of an n dimensional mixed characteristic local field
commutes with the Vostokov symbol of an n-1 dimensional
mixed characteristic local field.Here the author generalizes
this theorem to the case of a regular local ring A subject to
certain conditions. This is done by using Kato's reformulation
of the Vostokov symbol as a map from Milnor K-theory to
Fontaine-Messing cohomology.

Robert A. Bell <bell@cooper.edu>