Une preuve simple des conjectures de Langlands pour GL(n) sur un corps p-adique

By G. Henniart. 2000

558 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/dbe5cd778b1cf25c4ab7d2135a1ec69548709777

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. W. Gan
2. Tasho Kaletha
3. Peter Scholze
4. F. Shahidi
5. H. Grobner
6. J. Cogdell
7. Shuichiro Takeda
8. A. Raghuram

In Mathematical Physics

1. W. Gan
2. Tasho Kaletha
3. F. Shahidi
4. J. Cogdell
5. Atsushi Ichino
6. Peter Scholze
7. H. Grobner
8. Shuichiro Takeda

Citations in the corpus

• Functorial products for $\mathrm{GL}_2 \times \mathrm{GL}_3$ and the symmetric cube for $\mathrm{GL}_2$ (2002, methodology): “We put ρ = ρ1 ⊗ρ2, and we let π be the irreducible smooth representation of GL6(F) corresponding to ρ via the Langlands correspondence of [4], [ 5 ].”
• Functorial products for GL2×GL3 and functorial symmetric cube for GL2 (2000, unknown): “[4, 5 ,7,16]). The proof for the case v- 2 is similar, except that we use a quadratic base change.”
• A Refined Gross-Prasad Conjecture for Unitary Groups (2012, methodology): “In this case, the conjecture is known, and is a theorem of Harris-Taylor [16] and Henniart [17]:”
• Introduction to the Langlands Program (2000, methodology): “The local non-archimedean Langlands correspondence is treated in Harris-Taylor’s [16] (the introduction is very readable!) and in Henniart’s original work [18]; Murty’s Chapter 10 in [10] sketches the local”
• Riemann's zeta function and beyond (2003, unknown): “Now, thanks to the recent proof of the local Langlands correspondence by Harris and Taylor for GL(n) [14, 57, 59, 62, 63, 65, 101], the definitions at the ramified places can be made also.”
• Arithmetic invariants of discrete Langlands parameters (2010, background): “In light of this conjecture - which has been established for algebraic tori, as well as for some non-abelian groups like GLn(k) [23],[25], and SLn(k) [27] - it is reasonable to predict how representation-theoretic invariants of π relate to the arithmetic invariants of its parameters (φπ, ρπ).”
• Genericity and contragredience in the local Langlands correspondence (2012, methodology): “Let π be the representation of G(F) assigned to ξ ◦φ by the local Langlands correspondence [Harris and Taylor 2001; Henniart 2000].”
• On the local Bump-Friedberg L-function (2013, background): “′) the local factor attached to the pair (π,π′) in [JPS83]. We will denote by L(s,π) the factor L(s,π,1) where 1 is the trivial representation of the trivial group G0. It is a theorem from [HT01] and [H00] that there is a bijection φ: π→ φπ from the set of irreducible representations of Gn (up to is”
• Galois representations arising from some compact Shimura varieties (2011, background): “Harris-Taylor ([HT01]) and Henniart ([Hen00]) proved that there is a natural bijection”
• Functoriality for the quasisplit classical groups (2011, background): “defines an irreducible admissible unramified representation v of HN(kv) [17, 18 ].”
• Cuspidality of symmetric powers with applications (2002, background): “By the local Langlands correspondence (see [4], [5], [17]), Symm(πv) is well defined for everyv.”
• Formal degrees and local theta correspondence (2013, unknown): “Moreover, it follows from a result of Henniart [33] that γ Sh(2s, τ,R,ψ)= α · γ (2s,R ◦ φτ ,ψ) with some root of unity α, where φτ is the L-parameter associated to τ by the local Langlands correspondence [27, 32].”
• A Note on L-packets (2006, background): “It is the existence of a natural stable character f i! fG(`); f 2 H (G);”