On the Jacquet-Langlands correspondence in the cohomology of the Lubin-Tate deformation tower

Strauch, Matthias

Formes automorphes (I) - Actes du semestre du centre Émile Borel, printemps 2000, Astérisque, no. 298 (2005), pp. 391-410.

MR Zbl | 1 citation dans Numdam

@incollection{AST_2005__298__391_0,
     author = {Strauch, Matthias},
     title = {On the {Jacquet-Langlands} correspondence in the cohomology of the {Lubin-Tate} deformation tower},
     booktitle = {Formes automorphes (I) - Actes du semestre du centre \'Emile Borel, printemps 2000},
     editor = {Tilouine Jacques and Carayol Henri and Harris Michael and Vign\'eras Marie-France},
     series = {Ast\'erisque},
     pages = {391--410},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {298},
     year = {2005},
     mrnumber = {2141708},
     zbl = {1073.22010},
     language = {en},
     url = {http://www.numdam.org/item/AST_2005__298__391_0/}
}

TY  - CHAP
AU  - Strauch, Matthias
TI  - On the Jacquet-Langlands correspondence in the cohomology of the Lubin-Tate deformation tower
BT  - Formes automorphes (I) - Actes du semestre du centre Émile Borel, printemps 2000
AU  - Collectif
ED  - Tilouine Jacques
ED  - Carayol Henri
ED  - Harris Michael
ED  - Vignéras Marie-France
T3  - Astérisque
PY  - 2005
SP  - 391
EP  - 410
IS  - 298
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_2005__298__391_0/
LA  - en
ID  - AST_2005__298__391_0
ER  -

%0 Book Section
%A Strauch, Matthias
%T On the Jacquet-Langlands correspondence in the cohomology of the Lubin-Tate deformation tower
%B Formes automorphes (I) - Actes du semestre du centre Émile Borel, printemps 2000
%A Collectif
%E Tilouine Jacques
%E Carayol Henri
%E Harris Michael
%E Vignéras Marie-France
%S Astérisque
%D 2005
%P 391-410
%N 298
%I Société mathématique de France
%U http://www.numdam.org/item/AST_2005__298__391_0/
%G en
%F AST_2005__298__391_0

Strauch, Matthias. On the Jacquet-Langlands correspondence in the cohomology of the Lubin-Tate deformation tower, dans Formes automorphes (I) - Actes du semestre du centre Émile Borel, printemps 2000, Astérisque, no. 298 (2005), pp. 391-410. http://www.numdam.org/item/AST_2005__298__391_0/

Bibliographie
Cité par

[Ba] A. I. Badulescu - Orthogonalité des caractères pour $G L_{n}$ sur un corps local de caractéristique non nulle, Manuscripta Math. 101 (2000), no. 1, p. 49-70. | DOI | MR | Zbl

[Be1] V. G. Berkovich - Spectral theory and analytic geometry over non-Archimedean fields, Mathematical Surveys and Monographs, vol. 33, American Mathematical Society, Providence, RI, 1990. | MR | Zbl

[Be2] V. G. Berkovich, Étale cohomology for non-Archimedean analytic spaces, Publ. Math. Inst. Hautes Études Sci. 78 (1993), p. 5-161. | DOI | EuDML | Numdam | MR | Zbl

[Be3] V. G. Berkovich, Vanishing cycles for formal schemes. II, Invent. Math. 125 (1996), no. 2, p. 367-390. | DOI | MR | Zbl

[Be4] V. G. Berkovich, $ℓ$ -adic cohomology, preprint.

[Ber] P. Berthelot - Cohomologie rigide et cohomologie rigde à support propre, preprint.

[Bo] P. Boyer - Mauvaise réduction des variétés de Drinfeld et correspondance de Langlands locale, Invent. Math. 138 (1999), no. 3, p. 573-629. | DOI | MR | Zbl

[Bu] C. J. Bushnell - Induced representations of locally profinite groups, J. Algebra 134 (1990), no. 1, p. 104-114. | DOI | MR | Zbl

[BK] C. J. Bushnell & P. C. Kutzko - The admissible dual of $G L (N)$ via compact open subgroups, Annals of Mathematics Studies, vol. 129, Princeton University Press, Princeton, NJ, 1993. | MR | Zbl

[Ca1] H. Carayol - Nonabelian Lubin-Tate theory, in Automorphic forms, Shimura varieties, and $L$ -functions, vol. II (Ann Arbor, MI 1988), Perspect. Math., vol. 11, Academic Press, Boston, MA, 1990, p. 15-39. | MR | Zbl

[Ca2] H. Carayol, Preuve de la conjecture de Langlands locale pour $G L_{n}$ : travaux de Harris-Taylor et Henniart, in Séminaire Bourbaki 1998/99. Astérisque, vol. 266, Société Mathématique de France, 2000, Exp. n° 857, p. 191-243. | EuDML | Numdam | MR | Zbl

[Ch] C.-L. Chai - The group action on the closed fiber of the Lubin-Tate moduli space, Duke Math. J. 82 (1996), no. 3, p. 725-754. | MR | Zbl

[Co] L. Corwin - A construction of the supercuspidal representations of $G L_{n} (F), F p$ -adic, Trans. Amer. Math. Soc. 337 (1993), no. 1, p. 1-58. | MR | Zbl

[DKV] P. Deligne, D. Kazhdan & M.-F. Vignéras - Représentations des algèbres centrales simples $p$ -adiques, in Representations of reductive groups over a local field, Travaux en Cours, Hermann, Paris, 1984, p. 33-117. | MR | Zbl

[Dr] V. G. Drinfeld - Elliptic modules, Math. USSR-Sb. 23 (1974), no. 4, p. 561-592, English translation. | DOI | MR | Zbl

[Fa] G. Faltings - The trace formula and Drinfeld's upper halfplane, Duke Math. J. 76 (1994), no. 2, p. 467-481. | DOI | MR | Zbl

[HT] M. Harris & R. Taylor - The geometry and cohomology of some simple Shimura varieties. Annals of Mathematics Studies, vol. 151, Princeton University Press. Princeton, NJ, 2001, with an appendix by Vladimir G. Berkovich. | MR | Zbl

[He] G. Henniart - Correspondance de Langlands-Kazhdan explicite dans le cas non ramifié, Math. Nachr. 158 (1992). p. 7-26. | DOI | MR | Zbl

[HG] M. J. Hopkins & B. H. Gross - Equivariant vector bundles on the Lubin-Tate moduli space, in Topology and representation theory (Evanston, IL, 1992). Contemp. Math., vol. 158, American Mathematical Society, Providence, RI, 1994, p. 23-88. | DOI | MR | Zbl

[Hu1] R. Huber - A generalization of formal schemes and rigid analytic varieties, Math. Z. 217 (1994). no. 4, p. 513-551. | DOI | EuDML | MR | Zbl

[Hu2] R. Huber, Étale cohomology of rigid analytic varieties and adic spaces. Aspects of Mathematics, vol. E30, Friedr. Vieweg & Sohn, Braunschweig, 1996. | MR | Zbl

[Hu3] R. Huber, Swan representations associated with rigid analytic curves, J. reine angew. Math. 537 (2001), p. 165-234. | MR | Zbl

[dJ-vdP] A. J. De Jong & M. Van Der Put - Étale cohomology of rigid analytic spaces, Doc. Math. 1 (1996), p. 1-56, electronic. | EuDML | MR | Zbl

[Ka] N. M. Katz - Travaux de Dwork, in Séminaire Bourbaki, 24e année, 1911/1912, Lect. Notes in Math., vol. 317, Springer, Berlin, 1973, Exp. n° 409, p. 167-200. | EuDML | Numdam | MR | Zbl

[La] G. Laffaille - Construction de groupes $p$ -divisibles. Le cas de dimension $1$ , in Journées de Géométrie Algébrique de Rennes. (Rennes, 1918), vol. III Astérisque, vol. 65, Société Mathématique de France, 1979, p. 103-123. | Numdam | MR | Zbl

[Lu] J. Lubin - Finite subgroups and isogenies of one-parameter formal Lie groups, Ann. of Math. (2) 85 (1967), p. 296-302. | DOI | MR | Zbl

[LT] J. Lubin & J. T. Tate - Formal moduli for one-parameter formal Lie groups, Bull. Soc. math. France 94 (1966), p. 49-59. | DOI | EuDML | Numdam | MR | Zbl

[RZ] M. Rapoport & Th. Zink - Period spaces for $p$ -divisible groups, Annals of Mathematics Studies, vol. 141, Princeton University Press, Princeton, NJ, 1996. | MR | Zbl

[Ro] J. D. Rogawski - Representations of $G L (n)$ and division algebras over a $p$ -adic field, Duke Math. J. 50 (1983), no. 1, p. 161-196. | MR | Zbl

[Sa] P. J. Sally - Some remarks on discrete series characters for reductive $p$ -adic groups, in Representations of Lie groups (Kyoto, Hiroshima, 1986), Advanced Studies in Pure Mathematics, vol. 14, Academic Press, Boston, MA, 1988, p. 337-348. | MR | Zbl

[Yu] J.-K. Yu - On the moduli of quasi-canonical liftings, Compositio Math. 96 (1995), no. 3, p. 293-321. | EuDML | Numdam | MR | Zbl