Weil Group of A 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.
Read more about this topic: Weil Group
Famous quotes containing the words weil, group, number and/or field:
“Every perfect life is a parable invented by God.”
—Simone Weil (1909–1943)
“Remember that the peer group is important to young adolescents, and there’s nothing wrong with that. Parents are often just as important, however. Don’t give up on the idea that you can make a difference.”
—The Lions Clubs International and the Quest Nation. The Surprising Years, I, ch.5 (1985)
“At thirty years a woman asks her lover to give her back the esteem she has forfeited for his sake; she lives only for him, her thoughts are full of his future, he must have a great career, she bids him make it glorious; she can obey, entreat, command, humble herself, or rise in pride; times without number she brings comfort when a young girl can only make moan.”
—Honoré De Balzac (1799–1850)
“Vigil strange I kept on the field one night;
When you my son and my comrade dropt at my side that day,
One look I but gave which your dear eyes return’d with a look I
shall never forget,
One touch of your hand to mine O boy, reach’d up as you lay on the ground,”
—Walt Whitman (1819–1892)