Fix an odd prime number , and let be a collection of two-dimensional ordinary Galois representations defined over a finite field . Suppose that we are given newforms whose -adic representations
satisfy , and some other extra hypotheses. We shall determine the cyclotomic -invariant for the Selmer group attached to the product under the assumption that the -invariant is zero. If (i.e. the double product case) this allows us to deduce the Iwasawa Main Conjecture for if it is already known for a congruent pair , much as Greenberg and Vatsal did for (i.e. for elliptic cusp forms).
On fixe un nombre premier impair , et soit une famille de représentations galoisiennes ordinaires à deux dimensions définies sur un corps fini . On suppose données des formes modulaires primitives dont les représentations -adiques
satisfont , et quelques autres hypothèses supplémentaires. On détermine l’invariant cyclotomique pour le groupe de Selmer associé au produit sous l’hypothèse que l’invariant est nul. Si (c’est-à-dire dans le cas du double produit), cela nous permet de déduire la conjecture principale d’Iwasawa pour si elle est déjà connue pour une paire congruente , tout comme Greenberg et Vatsal l’ont fait pour (i.e. pour les formes modulaires paraboliques).
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Keywords: Galois representations, Iwasawa theory, $p$-adic $L$-functions.
Mot clés : Représentations galoisiennes, théorie d’Iwasawa, fonctions $L$ $p$-adiques.
Delbourgo, Daniel 1
@article{AIF_2024__74_2_451_0, author = {Delbourgo, Daniel}, title = {On the {Iwasawa} $\mu $-invariant and $\lambda $-invariant associated to tensor products of newforms}, journal = {Annales de l'Institut Fourier}, pages = {451--502}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {74}, number = {2}, year = {2024}, doi = {10.5802/aif.3593}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3593/} }
TY - JOUR AU - Delbourgo, Daniel TI - On the Iwasawa $\mu $-invariant and $\lambda $-invariant associated to tensor products of newforms JO - Annales de l'Institut Fourier PY - 2024 SP - 451 EP - 502 VL - 74 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3593/ DO - 10.5802/aif.3593 LA - en ID - AIF_2024__74_2_451_0 ER -
%0 Journal Article %A Delbourgo, Daniel %T On the Iwasawa $\mu $-invariant and $\lambda $-invariant associated to tensor products of newforms %J Annales de l'Institut Fourier %D 2024 %P 451-502 %V 74 %N 2 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3593/ %R 10.5802/aif.3593 %G en %F AIF_2024__74_2_451_0
Delbourgo, Daniel. On the Iwasawa $\mu $-invariant and $\lambda $-invariant associated to tensor products of newforms. Annales de l'Institut Fourier, Volume 74 (2024) no. 2, pp. 451-502. doi : 10.5802/aif.3593. https://aif.centre-mersenne.org/articles/10.5802/aif.3593/
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