Our investigation focuses on an additive analogue of the
Bloch–Gabber–Kato theorem which establishes a relation between the Milnor
-group
of a field of positive characteristic and a Galois cohomology group of the field.
Extending the Artin–Schreier–Witt theory, we present an isomorphism from the
Mackey product associated with the Witt group and the multiplicative groups to a
Galois cohomology group. As a result, we give a new expression for the torsion
subgroup of the Brauer group of a field, and more generally, the Kato homology
groups.
