## Algebraic Number Theory Notes : Local Fields

- Sam Mundy
- 2016

@inproceedings{Gruenberg2017CapitulationAT, title={Capitulation and transfer kernels}, author={Karl W. Gruenberg and Alfred Weiss}, year={2017} }

- Published 2017

If K/k is a finite Galois extension of number fields with Galois group G, then the kernel of the capitulation map Clk ~ ClK of ideal class groups is isomorphic to the kernel X(H) of the transfer map H/H’ ~ A, where H = Gal(K/k), A = Gal(K/K) and K is the Hilbert class field of K. H. Suzuki proved that when G is abelian, |G| divides |X(H)|. We call a finite… CONTINUE READING

### Presentations referencing similar topics