Given a dihedral Galois representation in characteristic , we establish (under some assumption) the existence of a CM newform, whose weight, level and Nebentypus we pin down, such that its -adic representation is congruent modulo to the one we started with.
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Pour une représentation galoisienne diédrale en caractéristique on établit (sous certaines hypothèses) l’existence d’une newform à multiplication complexe, dont on contrôle le poids, le niveau et le caractère, telle que la représentation -adique associée est congrue modulo à celle de départ.
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DOI: 10.5802/jtnb.1043
Classification: 11F80, 11R37
Keywords: Représentations galoisiennes, théorie du corps de classes, formes modulaires à multiplication complexe.
Author's affiliations:
@article{JTNB_2018__30_2_651_0, author = {Nicolas Billerey and Filippo A. E. Nuccio Mortarino Majno di Capriglio}, title = {Repr\'esentations galoisiennes di\'edrales et formes \`a multiplication complexe}, journal = {Journal de Th\'eorie des Nombres de Bordeaux}, pages = {651--670}, publisher = {Soci\'et\'e Arithm\'etique de Bordeaux}, volume = {30}, number = {2}, year = {2018}, doi = {10.5802/jtnb.1043}, zbl = {07081566}, language = {fr}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1043/} }
TY - JOUR TI - Représentations galoisiennes diédrales et formes à multiplication complexe JO - Journal de Théorie des Nombres de Bordeaux PY - 2018 DA - 2018/// SP - 651 EP - 670 VL - 30 IS - 2 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1043/ UR - https://zbmath.org/?q=an%3A07081566 UR - https://doi.org/10.5802/jtnb.1043 DO - 10.5802/jtnb.1043 LA - fr ID - JTNB_2018__30_2_651_0 ER -
Nicolas Billerey; Filippo A. E. Nuccio Mortarino Majno di Capriglio. Représentations galoisiennes diédrales et formes à multiplication complexe. Journal de Théorie des Nombres de Bordeaux, Volume 30 (2018) no. 2, pp. 651-670. doi : 10.5802/jtnb.1043. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1043/
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