The local Langlands conjecture for GSp(4)

Wee Teck Gan; Shuichiro Takeda

doi:http://doi.org/10.4007/annals.2011.173.3.12

Abstract

We prove the local Langlands conjecture for $\mathrm{GSp}_4(F)$ where $F$ is a non-archimedean local field of characteristic zero.

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@article {ST, MRKEY = {1212952}, AUTHOR = {Sally, Jr., Paul J. and Tadi{ć}, Marko}, TITLE = {Induced representations and classifications for {${\rm GSp}(2,F)$} and {${\rm Sp}(2,F)$}}, JOURNAL = {Mém. Soc. Math. France}, FJOURNAL = {Mémoires de la Société Mathématique de France. Nouvelle Série}, NUMBER = {52}, YEAR = {1993}, PAGES = {75--133}, ISSN = {0037-9484}, MRCLASS = {22E50}, MRNUMBER = {1212952}, MRREVIEWER = {Leticia Barchini}, ZBLNUMBER = {0784.22008}, }
[V] M. Vignéras, "Correspondances entre representations automorphes de ${ GL}(2)$ sur une extension quadratique de ${ GSp}(4)$ sur ${\bf Q}$, conjecture locale de Langlands pour ${ GSp}(4)$," in The Selberg Trace Formula and Related Topics, Providence, RI, 1986, pp. 463-527.

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@inproceedings {V, MRKEY = {0853573}, AUTHOR = {Vign{é}ras, Marie-France}, TITLE = {Correspondances entre representations automorphes de {${\rm GL}(2)$} sur une extension quadratique de {${\rm GSp}(4)$} sur {${\bf Q}$}, conjecture locale de {L}anglands pour {${\rm GSp}(4)$}}, BOOKTITLE = {The {S}elberg Trace Formula and Related Topics}, VENUE={{B}runswick, {M}aine, 1984}, SERIES = {Contemp. Math.}, VOLUME = {53}, PAGES = {463--527}, PUBLISHER = {Amer. Math. Soc.}, ADDRESS = {Providence, RI}, YEAR = {1986}, MRCLASS = {11S37 (11F70 22E50 22E55)}, MRNUMBER = {0853573}, MRREVIEWER = {J. G. M. Mars}, ZBLNUMBER = {0595.12009}, }
[Z] W. Zink, Letter to M.-F. Vigneras (1984).

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@misc{Z, author={Zink, W.}, TITLE={letter to {M.-F. V}igneras (1984)}, }

The local Langlands conjecture for GSp(4)

Abstract

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