Vol. 13, No. 4, 2019

 Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1944-7833 (e-only) ISSN: 1937-0652 (print) Author Index To Appear Other MSP Journals
Iwasawa theory for Rankin-Selberg products of $p$-nonordinary eigenforms

Kâzım Büyükboduk, Antonio Lei, David Loeffler and Guhan Venkat

Vol. 13 (2019), No. 4, 901–941
Abstract

Let $f$ and $g$ be two modular forms which are nonordinary at $p$. The theory of Beilinson–Flach elements gives rise to four rank-one nonintegral Euler systems for the Rankin–Selberg convolution $f\otimes g$, one for each choice of $p$-stabilisations of $f$ and $g$. We prove (modulo a hypothesis on nonvanishing of $p$-adic $L$-functions) that the $p$-parts of these four objects arise as the images under appropriate projection maps of a single class in the wedge square of Iwasawa cohomology, confirming a conjecture of Lei–Loeffler–Zerbes.

Furthermore, we define an explicit logarithmic matrix using the theory of Wach modules, and show that this describes the growth of the Euler systems and $p$-adic $L$-functions associated to $f\otimes g$ in the cyclotomic tower. This allows us to formulate “signed” Iwasawa main conjectures for $f\otimes g$ in the spirit of Kobayashi’s $±$-Iwasawa theory for supersingular elliptic curves; and we prove one inclusion in these conjectures under our running hypotheses.

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/ant

We have not been able to recognize your IP address 3.236.212.116 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

or by using our contact form.