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2019 Iwasawa theory for Rankin-Selberg products of $p$-nonordinary eigenforms
Kâzım Büyükboduk, Antonio Lei, David Loeffler, Guhan Venkat
Algebra Number Theory 13(4): 901-941 (2019). DOI: 10.2140/ant.2019.13.901

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 fg, 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 fg in the cyclotomic tower. This allows us to formulate “signed” Iwasawa main conjectures for fg in the spirit of Kobayashi’s ±-Iwasawa theory for supersingular elliptic curves; and we prove one inclusion in these conjectures under our running hypotheses.

Citation

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Kâzım Büyükboduk. Antonio Lei. David Loeffler. Guhan Venkat. "Iwasawa theory for Rankin-Selberg products of $p$-nonordinary eigenforms." Algebra Number Theory 13 (4) 901 - 941, 2019. https://doi.org/10.2140/ant.2019.13.901

Information

Received: 12 February 2018; Revised: 13 September 2018; Accepted: 10 February 2019; Published: 2019
First available in Project Euclid: 18 May 2019

zbMATH: 07059759
MathSciNet: MR3951583
Digital Object Identifier: 10.2140/ant.2019.13.901

Subjects:
Primary: 11R23
Secondary: 11F11, 11R20

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.13 • No. 4 • 2019
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