Geodesic
Iwasawa theory for symmetric squares of non-$p$-ordinary eigenforms
Documenta mathematica, Tome 26 (2021), pp. 1-63 Cet article a éte moissonné depuis la source EMS Press

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Let f be a normalized cuspidal eigen-newform of level coprime to p with ap​(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.
DOI : 10.4171/dm/808
Classification : 11F11, 11R23
Mots-clés : Iwasawa theory, Euler systems, elliptic modular forms, symmetric square representations, non-ordinary primes, Beilinson-Flach classes 
@article{10_4171_dm_808,
     author = {Antonio Lei and Guhan Venkat and Kazim B\"uy\"ukboduk},
     title = {Iwasawa theory for symmetric squares of non-$p$-ordinary eigenforms},
     journal = {Documenta mathematica},
     pages = {1--63},
     year = {2021},
     volume = {26},
     doi = {10.4171/dm/808},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/808/}
}
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Antonio Lei; Guhan Venkat; Kazim Büyükboduk. Iwasawa theory for symmetric squares of non-$p$-ordinary eigenforms. Documenta mathematica, Tome 26 (2021), pp. 1-63. doi: 10.4171/dm/808

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