In this paper, we extend the results of Ribet and Taylor on level-raising for algebraic modular forms on the multiplicative group of a definite quaternion algebra over a totally real field . We do this for automorphic representations of an arbitrary reductive group over , which is compact at infinity. In the special case where is an inner form of over , we use this to produce congruences between Saito-Kurokawa forms and forms with a generic local component.
Dans cet article, on étend des résultats d’augmentation du niveau de Ribet et Taylor, au cas de formes modulaires algébriques pour une algèbre à division sur un corps totalement réel . On travaille avec des représentations automorphes d’un groupe réductif sur , compact à l’infini. Dans le cas particulier où est une forme intérieure de sur , on utilise ces résultats pour construire des congruences entre des formes de Saito-Kurokawa et des formes avec des composantes locales génériques.
Keywords: Level-raising, algebraic modular forms
Mot clés : augmentation du niveau, formes modulaires algébriques
@article{AIF_2006__56_6_1735_0, author = {Mazanti Sorensen, Claus}, title = {A generalization of level-raising congruences for algebraic modular forms}, journal = {Annales de l'Institut Fourier}, pages = {1735--1766}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {56}, number = {6}, year = {2006}, doi = {10.5802/aif.2226}, mrnumber = {2282674}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2226/} }
TY - JOUR AU - Mazanti Sorensen, Claus TI - A generalization of level-raising congruences for algebraic modular forms JO - Annales de l'Institut Fourier PY - 2006 SP - 1735 EP - 1766 VL - 56 IS - 6 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2226/ DO - 10.5802/aif.2226 LA - en ID - AIF_2006__56_6_1735_0 ER -
%0 Journal Article %A Mazanti Sorensen, Claus %T A generalization of level-raising congruences for algebraic modular forms %J Annales de l'Institut Fourier %D 2006 %P 1735-1766 %V 56 %N 6 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2226/ %R 10.5802/aif.2226 %G en %F AIF_2006__56_6_1735_0
Mazanti Sorensen, Claus. A generalization of level-raising congruences for algebraic modular forms. Annales de l'Institut Fourier, Volume 56 (2006) no. 6, pp. 1735-1766. doi : 10.5802/aif.2226. http://archive.numdam.org/articles/10.5802/aif.2226/
[1] Congruences endoscopiques et représentations galoisiennes (2002) (thesis, Université Paris XI - Orsay. http://www.math.columbia.edu/~jbellaic/)
[2] Le <<centre>> de Bernstein, Representations of reductive groups over a local field (Travaux en Cours), Hermann, Paris, 1984, pp. 1-32 (Edited by P. Deligne) | MR | Zbl
[3] Personal communication (November 2004)
[4] Representations of reductive -adic groups: Localization of Hecke algebras and applications, J. London Math. Soc. (2), Volume 63 (2001) no. 2, pp. 364-386 | DOI | MR | Zbl
[5] Introduction to the theory of admissible representations of -adic reductive groups (1995) (preprint. , http://www.math.wisc.edu/~ram/p-adic-book.ps)
[6] On Ribet’s level-raising theorem for , Amer. J. Math., Volume 122 (2000) no. 6, pp. 1265-1287 | DOI | MR | Zbl
[7] Formes modulaires de poids , Ann. Sci. École Norm. Sup. (4), Volume 7 (1974), pp. 507-530 | Numdam | MR | Zbl
[8] The geometry and cohomology of some simple Shimura varieties, Annals of Mathematics Studies, 151, Princeton University Press, Princeton, NJ, 2001 (With an appendix by Vladimir G. Berkovich) | MR | Zbl
[9] The local Langlands correspondence: The non-Archimedean case, Motives (Seattle, WA, 1991) (Proc. Sympos. Pure Math.), Volume 55, Amer. Math. Soc., Providence, RI, 1994, pp. 365-391 | MR | Zbl
[10] Sur la cohomologie à supports compacts des variétés de Shimura pour , Compositio Math., Volume 105 (1997) no. 3, pp. 267-359 | DOI | MR | Zbl
[11] Local level-raising for (2001) (thesis, Harvard)
[12] Level-raising congruences in the representation theory of reductive groups over local fields (2003) (thesis, Princeton)
[13] Congruence relations between modular forms, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983), PWN, Warsaw (1984), pp. 503-514 | MR | Zbl
[14] Induced representations and classifications for and , Mém. Soc. Math. France (N.S.) (1993) no. 52, pp. 75-133 | Numdam | MR | Zbl
[15] Iwahori-spherical representations of and Siegel modular forms of degree 2 with square-free level, J. Math. Soc. Japan, Volume 57 (2005) no. 1, pp. 259-293 | DOI | MR | Zbl
[16] Two letters on quaternions and modular forms (mod ), Israel J. Math., Volume 95 (1996), pp. 281-299 (With introduction, appendix and references by R. Livné) | DOI | MR | Zbl
[17] Sur les déformations -adiques de certaines représentations automorphes (May 2004) (preprint)
[18] On Galois representations associated to Hilbert modular forms, Invent. Math., Volume 98 (1989) no. 2, pp. 265-280 | DOI | MR | Zbl
[19] Representations of Galois groups associated to Hilbert modular forms, Automorphic forms, Shimura varieties, and -functions, Vol. II (Ann Arbor, MI, 1988) (Perspect. Math.), Volume 11, Academic Press, Boston, MA, 1990, pp. 323-336 | MR | Zbl
[20] Four dimensional Galois representations (preprint, http://www.mathi.uni-heidelberg.de/~weissaue/papers.html)
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