Skip to main content Accessibility help
×
Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-23T02:01:48.318Z Has data issue: false hasContentIssue false

4 - Effective local Langlands correspondence

Published online by Cambridge University Press:  05 October 2014

Colin J. Bushnell
Affiliation:
King's College London
Fred Diamond
Affiliation:
King's College London
Payman L. Kassaei
Affiliation:
King's College London
Minhyong Kim
Affiliation:
University of Oxford
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] J., Arthur and L., Clozel, Simple algebras, base change, and the advanced theory of the trace formula, Annals of Math. Studies, vol. 120, Princeton University Press, 1989.
[2] C.J., Bushnell and G., Henniart, Local tame lifting for GL(n) I: simple characters, Publ. Math. IHES 83 (1996), 105–233.Google Scholar
[3] C.J., Bushnell, Local Rankin-Selberg convolution for GL(n): divisibility of the conductor, Math. Ann. 321 (2001), 455–461.Google Scholar
[4] C.J., Bushnell, On certain dyadic representations. Appendix to H. Kim and F. Shahidi, Functorial products for GL(2) × GL(3) and functorial symmetric cube for GL(2), Annals of Math. (2) 155 (2002), 883–893.Google Scholar
[5] C.J., Bushnell, Local tame lifting for GL(n) IV: simple characters and base change, Proc. London Math. Soc. 87 (2003), 337–362.Google Scholar
[6] C.J., Bushnell, Local tame lifting for GL(n) III: explicit base change and Jacquet-Langlands correspondence, J. reine angew. Math. 508 (2005), 39–100.Google Scholar
[7] C.J., Bushnell, The essentially tame local Langlands correspondence, I J. Amer. Math. Soc. 18 (2005), 685–710.Google Scholar
[8] C.J., Bushnell, The essentially tame local Langlands correspondence, II: totally ramified representations, Compositio Mathematica 141 (2005), 979–1011.Google Scholar
[9] C.J., Bushnell, The local Langlands Conjecture for GL(2) Grundlehren der mathematischen Wissenschaften, vol. 335, Springer, 2006.
[10] C.J., Bushnell, The essentially tame local Langlands correspondence, III: the general case, Proc. London Math. Soc. (3) 101 (2010), 497–553.Google Scholar
[11] C.J., Bushnell, The essentially tame local Jacquet-Langlands correspondence, Pure App. Math. Quarterly 7 (2011), 469–538.Google Scholar
[12] C.J., Bushnell, Explicit functorial correspondences for level zero representations of p-adic linear groups, J. Number Theory 131 (2011), 309–331.Google Scholar
[13] C.J., Bushnell, To an effective local Langlands correspondence, Memoirs Amer. Math. Soc., to appear. arXiv:1103.5316.
[14] C.J., Bushnell, Modular local Langlands correspondence for GLn, Int. Math. Res. Not. (2013), doi: 10.1093/imrn/rnt063.
[15] C.J., Bushnell and P.C., Kutzko, The admissible dual of GL(N) via compact open subgroups, Annals of Math. Studies, vol. 129, Princeton University Press, 1993.
[16] G., Glauberman, Correspondences of characters for relatively prime operator groups, Canadian J. Math. 20 (1968), 1465–1488.Google Scholar
[17] J.A., Green, The characters of the finite general linear groups, Trans. Amer. Math. Soc. 80 (1955), 402–447.Google Scholar
[18] M., Harris and R., Taylor, On the geometry and cohomology of some simple Shimura varieties, Annals of Math. Studies, vol. 151, Princeton University Press, 2001.
[19] G., Henniart, La conjecture locale de Langlands pour GL(3), Mém. Soc. Math. France, nouvelle série 11/12 (1984).Google Scholar
[20] G., Henniart, Caractérisation de la correspondance de Langlands locale par les facteurs ε de paires, Invent. Math. 113 (1993), 339–356.Google Scholar
[21] G., Henniart, Une preuve simple des conjectures locales de Langlands pour GLn sur un corps p-adique, Invent. Math. 139 (2000), 439–455.Google Scholar
[22] G., Henniart and R., Herb, Automorphic induction for GL(n) (over local nonarchimedean fields), Duke Math. J. 78 (1995), 131–192.Google Scholar
[23] G., Henniart and B., Lemaire, Changement de base et induction automorphe pour GLn en caractéristique non nulle, Mém. Soc. Math. France 108 (2010).Google Scholar
[24] H., Jacquet, I.I., Piatetskii-Shapiro and J.A., Shalika, Rankin-Selberg convolutions, Amer. J. Math. 105 (1983), 367–483.Google Scholar
[25] J.-L., Kim, Supercuspidal representations: an exhaustion theorem, J. Amer. Math. Soc. 20 (2007), 273–320.Google Scholar
[26] P.C., Kutzko, The Langlands conjecture for GL2 of a local field, Annals of Math. 112 (1980), 381–412.Google Scholar
[27] G., Laumon, M., Rapoport and U., Stuhler, D-elliptic sheaves and the Langlands correspondence, Invent. Math. 113 (1993), 217–338.Google Scholar
[28] C., Mœglin, Sur la correspondance de Langlands-Kazhdan, J. Math. Pures et Appl. (9) 69 (1990), 175–226.Google Scholar
[29] A., Moy and G., Prasad, Unrefined minimal K -types for p-adic groups, Invent. Math. 116 (1994), 393-408.Google Scholar
[30] I., Reiner, Maximal orders, Oxford University Press, 2003.
[31] V., Sécherre and S., Stevens, Représentations lisses de GLm(D), IV: représentations supercuspidales. J. Inst. Math. Jussieu 7 (2008), 527–574.Google Scholar
[32] F., Shahidi, Fourier transforms of intertwining operators and Plancherel measures for GL(n), Amer. J. Math. 106 (1984), 67–111.Google Scholar
[33] A., Silberger and E.-W., Zink, An explicit matching theorem for level zero discrete series of unit groups of р-adic simple algebras, J. reine angew. Math. 585 (2005), 173–235.Google Scholar
[34] S.A.R., Stevens, The supercuspidal representations of p-adic classical groups, Invent. Math. 172 (2008), 289–352.Google Scholar
[35] J., Tits, Reductive groups over local fields, Automorphic forms, representations and L-functions (A., Borel and W., Casselman, eds.), Proc. Symp. Pure Math.,vol. 33(1), Amer. Math. Soc., 1979, pp. 29–69.
[36] J.-K., Yu, Construction of tame supercuspidal representations, J. Amer. Math. Soc. 14 (2001), 579–622.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×