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

Kâzım Büyükboduk, Antonio Lei, Guhan Venkat

Published 2018-07-30Version 1

Our main goal in this article is to prove a divisibility statement in the Iwasawa main conjectures for symmetric squares of non-$p$-ordinary eigenforms (twisted by an auxiliary Dirichlet character). This task is carried out with the aid of Beilinson-Flach elements, which need to be suitably modified to obtain their integral counterparts. The key technical novelty is a significant improvement of the signed factorization procedure employed in the semi-ordinary Rankin-Selberg products, dwelling on ideas of Perrin-Riou on higher rank Euler systems.