The focus of
this course is local class field theory, to be followed in the spring
term by its companion course Math 160c covering global class field
theory.
We will study local fields, their ramification and Galois groups,
Galois cohomology, Brauer groups, local duality, the invariant map, the
Euler characteristic formula and possibly explicit class field theory
in LubinTate towers and local Galois representations.
The course assumes a working knowledge of abstract algebra, Galois
theory and basic algebraic number theory. Math 160a and Math 120b are
necessary.
