8 Lubin–Tate theory

For the rest of the course, we will indicate how one can explicitly construct the

field K

ab

and the map Art

K

.

There are many ways we can approach local class field theory. The approach

we use, using Lubin–Tate theory, is the most accessible one. Another possible

approach is via Galois cohomology. This, however, relies on more advanced

machinery, namely Galois cohomology.