1. The CM field and the class number splitting
This chapter develops the CM extension \mathbb{Q}(\zeta_p)/\mathbb{Q}(\zeta_p)^+
and proves that the class number of the maximal real subfield divides the full
class number, so that the relative class number \hminus may be defined by
honest division.
- 1.1. The maximal real subfield
- 1.2. The class numbers h, h-plus, and h-minus
- 1.3. The class-group map and faithful-flat descent
- 1.4. Conjugation on principal generators
- 1.5. A conjugation-fixed associate and descent to the real ring of integers
- 1.6. Injectivity of the class-group map and the definition of h-minus