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arXiv · 1807.11517

Iwasawa theory for Symmetric Square of non-$p$-ordinary eigenforms

Kâzım Büyükboduk·Antonio Lei·Guhan Venkat
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Abstract

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 man 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 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.

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Kâzım Büyükboduk, Antonio Lei, Guhan Venkat. 2018-07-30. Iwasawa theory for Symmetric Square of non-$p$-ordinary eigenforms. https://doi.org/10.25537/dm.2021v26.1-63

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