that act as a power of the Frobenius automorphism on the constant field (the union of all finite subfields).

Number field

For number fields there is no known "natural" construction of the Weil group without using cocycles to construct the extension. The map from the Weil group to the Galois group is surjective, and its kernel is the connected component of the identity of the Weil group, which is quite complicated.

Weil-Deligne group

The Weil-Deligne group scheme (or simply Weil-Deligne group) W´_K

1.Previous
3.Next