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>