The local Langlands conjecture for $\text{GSp}(4)$

DOI10.4007/annals.2011.173.3.12zbMath1230.11063arXiv0706.0952OpenAlexW2803730352WikidataQ123160012 ScholiaQ123160012MaRDI QIDQ640778

Shuichiro Takeda, Gan, Wee Teck

Publication date: 20 October 2011

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0706.0952

zbMATH Keywords

local Langlands correspondence Weil-Deligne group theta correspondence

Mathematics Subject Classification ID

Representations of Lie and linear algebraic groups over local fields (22E50) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Langlands-Weil conjectures, nonabelian class field theory (11S37)

Related Items

Euler systems for $\mathrm{GSp}(4)$, The distinction problems for $\operatorname{Sp}_4$ and $\operatorname{SO}_{3,3}$, Theta correspondences for 𝐺𝑆𝑝(4), Unnamed Item, On the theta correspondence for (𝐺𝑆𝑝(4),𝐺𝑆𝑂(4,2)) and Shalika periods, Theta lifts of Bianchi modular forms and applications to paramodularity, On the resolution of reductive monoids and multiplicativity of $\gamma $-factors, Generic level $p$ Eisenstein congruences for $\mathrm{GSp}_{4}$, $L$-factor of irreducible $\chi_1 \times\chi_2 \rtimes\sigma$, A geometric Jacquet-Langlands correspondence for paramodular Siegel threefolds, Deformation Theory and Local-Global Compatibility of Langlands Correspondences, The local Langlands conjecture for $p$-adic $\mathrm{GSpin}_{4}$, $\mathrm{GSpin}_{6}$, and their inner forms, A local converse theorem for $\mathrm{U}(2,2)$, The Local Langlands Conjecture for, Companion forms for unitary and symplectic groups, An explicit lifting construction of CAP forms on O(1,5), ON FUNDAMENTAL FOURIER COEFFICIENTS OF SIEGEL CUSP FORMS OF DEGREE 2, Equidistribution theorems for holomorphic Siegel modular forms for $\mathrm{GSp}_4$; Hecke fields and $n$-level density, On local zeta-integrals for $\mathrm{GSp}(4)$ and $\mathrm{GSp}(4) \times \mathrm{GL}(2)$, Periods of automorphic forms, poles of $L$-functions and functorial lifting, On the images of Galois representations attached to low weight Siegel modular forms, On Petersson norms of generic cusp forms and special values of adjoint L -functions for GSp4, On Deligne's conjecture for symmetric fourth $L$-functions of Hilbert modular forms, Exceptional poles of local spinor L‐functions of GSp(4) with anisotropic Bessel models, Howe duality and dichotomy for exceptional theta correspondences, SYMMETRIC POWER CONGRUENCE IDEALS AND SELMER GROUPS, Packet structure and paramodular forms, Descent Construction for GSpin groups, ON THE LOCAL LANGLANDS CORRESPONDENCE FOR SPLIT CLASSICAL GROUPS OVER LOCAL FUNCTION FIELDS, Lefschetz trace formula and $\ell$-adic cohomology of Rapoport-Zink tower for $\mathrm{GSp}(4)$, Depth-zero supercuspidal $L$-packets for inner forms of $\mathrm{GSp}_4$, The Prasad conjectures for $\mathrm{GSp}_4$ and $\mathrm{PGSp}_4$, The local Langlands conjecture for $\mathrm{GSp}(4)$. III: Stability and twisted endoscopy, Formal degrees and local theta correspondence, Descending congruences of theta lifts on $\mathrm{GSp}_{4}$, The conservation relation for cuspidal representations, Theta dichotomy for the genuine unramified principal series of $\widetilde{\text{Sp}}_2(F)$, Local Langlands correspondence for even orthogonal groups via theta lifts, Local Langlands correspondence for unitary groups via theta lifts, Representations of metaplectic groups I: epsilon dichotomy and local Langlands correspondence, On central critical values of the degree four $L$-functions for $\mathrm{GSp}(4)$: a simple trace formula, Jacquet-Langlands-Shimizu correspondence for theta lifts to $\mathrm{GSp}(2)$ and its inner forms II: an explicit formula for Bessel periods and the non-vanishing of theta lifts, Symplectic supercuspidal representations and related problems, On the standard $L$-function for $\mathrm{GSp}_{2n}\times\mathrm{GL}_1$ and algebraicity of symmetric fourth $L$-values for $\mathrm{GL}_2$, Formulas for central values of twisted spin $L$-functions attached to paramodular forms, The $\mathrm{PGSp}_{1,1}(\mathbb{A})$-distinguished representations, The Conjectural Relation Between Generalized Shalika Models on $$\mathop{\mathrm{SO}}\nolimits _{4n}(F)$$ and Symplectic Linear Models on $$\mathop{\mathrm{Sp}}\nolimits _{4n}(F)$$ : A Toy Example, On twisted exterior and symmetric square $\gamma$-factors, AN EQUIDISTRIBUTION THEOREM FOR HOLOMORPHIC SIEGEL MODULAR FORMS FOR AND ITS APPLICATIONS, On the adjoint $L$-function of the $p$-adic $\text{GSp}(4)$, Arthur's multiplicity formula for $\mathrm{GSp}_4$ and restriction to $\mathrm{Sp}_4$, Abelian surfaces over totally real fields are potentially modular, Siegel modular forms of degree two attached to Hilbert modular forms, Higher Hida theory and $p$-adic $L$-functions for $\mathrm{GSp}_4$, Special values of L-functions for Saito–Kurokawa lifts, Higher coherent cohomology and $p$-adic modular forms of singular weights, Algebraicity of critical values of adjoint $L$-functions for $\mathrm{GSp}_4$, Book Review: Automorphic representations and L-functions for the general linear group. Volume I; Automorphic representations and L-functions for the general linear group. Volume II, Paramodular forms of level 16 and supercuspidal representations, Local factors of nongeneric supercuspidal representations of $\mathrm{GSp}_4$, Ordinary representations of $G(\mathbb{Q}_p)$ and fundamental algebraic representations, Galois representations attached to automorphic forms on over fields

Cites Work

The local Langlands conjecture for \(\text{GSp}(4)\)