The Artin Symbol as a Canonical Capitulation Map

Details The Artin Symbol as a Canonical Capitulation Map The Artin Symbol as a Canonical Capitulation Map

2009-05-18

arxiv.org/abs/0905.2866v1

Mathematics

Number Theory

8 pages

Scientific paper

We show that there is a canonical, order preserving map $\psi$ of lattices of subgroups, which maps the lattice $\Sub(A)$ of subgroups of the ideal class group of a galois number field $\K$ into the lattice $\Sub(\KH/\K)$ of subfields of the Hilbert class field. Furthermore, this map is a capitulation map in the sense that all the primes in the classes of $A' \subset A$ capitulate in $\psi(A')$. In particular we have a new, strong version of the generalized Hilbert 94 Theorem, which confirms the result of Myiake and adds more structure to (part) of the capitulation kernel of subfields of $\KH$.

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