nLab Weil group


Not to be confused with Weyl group.


Group Theory




Let FF be a p-adic field, with residue field denoted κ\kappa.

The Weil group W FW_F is the subgroup of the Galois group Gal(F¯/F)\mathrm{Gal}(\overline{F}/F) defined as the inverse image of Frobenius automorphisms Frob Gal(κ¯/κ)\mathrm{Frob}^{\mathbb{Z}}\subset \mathrm{Gal}(\overline{\kappa}/\kappa) under the surjective map Gal(F¯/F)Gal(κ¯/κ)\mathrm{Gal}(\overline{F}/F)\to\mathrm{Gal}(\overline{\kappa}/\kappa).


  • John Tate, Section 1 in: Number theoretic background, in: Automorphic forms, representations and L-functions, Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore. (1977), Part 2, Proc. Sympos. Pure Math., XXXIII, pages 3–26. Amer. Math. Soc., Providence, RI (ISBN:978-0-8218-3371-1, pdf, pdf)

See also:

Last revised on April 23, 2021 at 06:37:50. See the history of this page for a list of all contributions to it.