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Weil group

Not to be confused with Weyl group.


Context

Group Theory

Arithmetic

Contents

Definition

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).

References

See also: