Capitulation in the cyclotomic ℤ2 extension of CM number fields

KATHARINA MÜLLER
  • Mathematical Proceedings of the Cambridge Philosophical Society, February 2018, Cambridge University Press
  • DOI: 10.1017/s0305004118000026

Relations of p class groups on different layers of the 2 cyclotomic extension of CM number fields

What is it about?

For odd primes there is a good notion how to define the minus part of the p class group of a CM number field. The classical definition fails for p=2. The aim of this paper is to give a definition of the minus part for p=2 and to establish properties known for odd primes for p=2 as well.

Why is it important?

The paper shows that there is a definition of the minus part of the class group which is equivalent to the classical one in the case of odd primes. It could be tool to adopt proofs of results only known for odd primes for p=2 as well.

Perspectives

Katharina Müller (Author)
Georg-August-Universitaet Goettingen

One of the main results is that Iwasawas Invariant mu=0 for the cyclotomic Z_2 extension of a CM number field if and only if mu^- is zero (where mu^- is the corresponding Invariant for the minus part). Since the ideal lift is injective on the minus part one clud might use this result to show that mu=0.

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http://dx.doi.org/10.1017/s0305004118000026

The following have contributed to this page: Katharina Müller