Weil Group of A Local Field
For local of characteristic p > 0, the Weil group is the subgroup of the absolute Galois group of elements that act as a power of the Frobenius automorphism on the constant field (the union of all finite subfields).
For p-adic fields the Weil group is a dense subgroup of the absolute Galois group, consisting of all elements whose image in the Galois group of the residue field is an integral power of the Frobenius automorphism.
More specifically, in these cases, the Weil group does not have the subspace topology, but rather a finer topology. This topology is defined by giving the inertia subgroup its subspace topology and imposing that it be an open subgroup of the Weil group. (The resulting topology is "locally profinite" one.)
Read more about this topic: Weil Group
Famous quotes containing the words weil, group, local and/or field:
“I am not a Catholic; but I consider the Christian idea, which has its roots in Greek thought and in the course of the centuries has nourished all of our European civilization, as something that one cannot renounce without becoming degraded.”
—Simone Weil (1909–1943)
“No group and no government can properly prescribe precisely what should constitute the body of knowledge with which true education is concerned.”
—Franklin D. Roosevelt (1882–1945)
“The local is a shabby thing. There’s nothing worse than bringing us back down to our own little corner, our own territory, the radiant promiscuity of the face to face. A culture which has taken the risk of the universal, must perish by the universal.”
—Jean Baudrillard (b. 1929)
“How sweet I roam’d from field to field
And tasted all the summer’s pride,
Till I the Prince of Love beheld
Who in the sunny beams did glide!”
—William Blake (1757–1827)