1.Previous
3.Next

defined to be the inverse limit of the Weil groups of all the layersG/F, for F an open subgroup of G.

The reciprocity map of the class formation (G, A) induces an isomorphism from A^G to the abelianization of the Weil group.

Archimedean local field

For archimedean local fields the Weil group is easy to describe: for C it is the group C^× of non-zero complex numbers, and for R it is a non-split extension of the Galois group of order

1.Previous
3.Next