##### General SectionIwasawa theory for class groups of CM fields with p = 2

Review articleOpen access###### Mahiro Atsuta - No affiliation found

**2019/11/01**DOI: 10.1016/j.jnt.2019.04.023

*Full-length article***Journal:**Journal of Number Theory

##### Abstract:

AbstractIn this paper, we study Iwasawa theory for p=2. First of all, we show that the classical Iwasawa main conjecture holds true even for p=2 over a totally real field k assuming μ=0 and Leopoldt's conjecture. Using the Iwasawa main conjecture, we study the 2-component of the ideal class group of a CM-field K of finite degree as a Galois module. More precisely, for a CM-field K which is cyclic over the base field k, we determine the Fitting ideal of the minus quotient of the 2-component of the ideal class group. In particular, when k=Q and K/Q is imaginary and cyclic, we prove that the Fitting ideal coincides with the Stickelberger ideal.

Request full text