We study the endomorphism algebra of the motive attached to a non-CM elliptic modular cusp form. We prove that this algebra has a sub-algebra isomorphic to a certain crossed product algebra . The Tate conjecture predicts that is the full endomorphism algebra of the motive. We also investigate the Brauer class of . For example we show that if the nebentypus is real and is a prime that does not divide the level, then the local behaviour of at a place lying above is essentially determined by the corresponding valuation of the -th Fourier coefficient of the form.
On étudie l’algèbre des endomorphismes du motif associé à une forme modulaire parabolique sans une multiplication complexe. On démontre que cette algèbre possède une sous-algèbre isomorphe à une algèbre de type produit croisé. La conjecture de Tate prédit que est l’algèbre des endomorphismes du motif. On étudie également la classe de Brauer de . Par exemple quand le nebentypus est réel et est un nombre premier qui ne divise pas le niveau, on démontre que le comportement local de en une place dominant est déterminé essentiellement par la valuation correspondante du -ième coefficient de Fourier de la forme.
Keywords: endomorphism algebras, modular motives, Tate conjecture, filtered $(\phi ,N)$-modules, Newton polygons, symbols
Mot clés : algèbres d’endomorphismes, motifs modulaires, conjecture de Tate, $(\phi ,N)$- modules filtrés, polygones de Newton, symboles
Brown, Alexander F. 1; Ghate, Eknath P. 1
@article{AIF_2003__53_6_1615_0, author = {Brown, Alexander F. and Ghate, Eknath P.}, title = {Endomorphism algebras of motives attached to elliptic modular forms}, journal = {Annales de l'Institut Fourier}, pages = {1615--1676}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {53}, number = {6}, year = {2003}, doi = {10.5802/aif.1989}, zbl = {1050.11062}, mrnumber = {2038777}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1989/} }
TY - JOUR AU - Brown, Alexander F. AU - Ghate, Eknath P. TI - Endomorphism algebras of motives attached to elliptic modular forms JO - Annales de l'Institut Fourier PY - 2003 SP - 1615 EP - 1676 VL - 53 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1989/ DO - 10.5802/aif.1989 LA - en ID - AIF_2003__53_6_1615_0 ER -
%0 Journal Article %A Brown, Alexander F. %A Ghate, Eknath P. %T Endomorphism algebras of motives attached to elliptic modular forms %J Annales de l'Institut Fourier %D 2003 %P 1615-1676 %V 53 %N 6 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1989/ %R 10.5802/aif.1989 %G en %F AIF_2003__53_6_1615_0
Brown, Alexander F.; Ghate, Eknath P. Endomorphism algebras of motives attached to elliptic modular forms. Annales de l'Institut Fourier, Volume 53 (2003) no. 6, pp. 1615-1676. doi : 10.5802/aif.1989. https://aif.centre-mersenne.org/articles/10.5802/aif.1989/
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