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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf sheaves simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthornLab edit announcer
   • CommentTimeApr 23rd 2021
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexPage created, but author did not leave any comments. Anonymous <a href="https://ncatlab.org/nlab/revision/Weil+group/1">v1</a>, <a href="https://ncatlab.org/nlab/show/Weil+group">current</a>

   Page created, but author did not leave any comments.

   Anonymous

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeApr 23rd 2021
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   Author: Urs
   Format: MarkdownItexI gave the empty entry some rudimentary content, using the material from *[[local Langlands correspondence]]*: Added the words *[[Frobenius automorphism]]* to where $Frob$ appears, but check: > The *Weil group* $W_F$ is the [[subgroup]] of the [[Galois group]] $\mathrm{Gal}(\overline{F}/F)$ defined as the [[inverse image]] of [[Frobenius automorphisms]] $\mathrm{Frob}^{\mathbb{Z}}\subset \mathrm{Gal}(\overline{\kappa}/\kappa)$ under the [[surjective]] map $\mathrm{Gal}(\overline{F}/F)\to\mathrm{Gal}(\overline{\kappa}/\kappa)$. <a href="https://ncatlab.org/nlab/revision/diff/Weil+group/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/Weil+group/2">v2</a>, <a href="https://ncatlab.org/nlab/show/Weil+group">current</a>

   I gave the empty entry some rudimentary content, using the material from local Langlands correspondence:

   Added the words Frobenius automorphism to where $Frob$ appears, but check:

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

   diff, v2, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeApr 23rd 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[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](https://bookstore.ams.org/pspum-33-2), [pdf](http://www.math.ucsd.edu/~csorense/teaching/math205/Tate_Weil.pdf), [[TateNumberTheory.pdf:file]]) <a href="https://ncatlab.org/nlab/revision/diff/Weil+group/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/Weil+group/3">v3</a>, <a href="https://ncatlab.org/nlab/show/Weil+group">current</a>

   added pointer to:

   • 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, TateNumberTheory.pdf:file)

   diff, v3, current