Geodesic
Iwasawa theory for symmetric squares of non-$p$-ordinary eigenforms
Documenta mathematica, Tome 26 (2021), pp. 1-63.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Let $f$ be a normalized cuspidal eigen-newform of level coprime to $p$ with $a_p(f)=0$. We formulate both integral signed Iwasawa main conjectures and analytic Iwasawa main conjectures attached to the symmetric square motive of $f$ twisted by an auxiliary Dirichlet character. We show that the Beilinson-Flach elements attached to the symmetric square motive factorize into integral signed Beilinson-Flach elements, giving evidence towards the existence of a rank-two Euler system predicted by Perrin-Riou. We use these integral elements to prove one inclusion in the integral and analytic Iwasawa main conjectures.
Classification : 11R23, 11F11
Keywords: Iwasawa theory, elliptic modular forms, symmetric square representations, non-ordinary primes, Beilinson-Flach classes, Euler systems 
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     author = {B\"uy\"ukboduk, Kazim and Lei, Antonio and Venkat, Guhan},
     title = {Iwasawa theory for symmetric squares of non-\(p\)-ordinary eigenforms},
     journal = {Documenta mathematica},
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     publisher = {mathdoc},
     volume = {26},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a56/}
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Büyükboduk, Kazim; Lei, Antonio; Venkat, Guhan. Iwasawa theory for symmetric squares of non-\(p\)-ordinary eigenforms. Documenta mathematica, Tome 26 (2021), pp. 1-63. http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a56/