Iwasawa Main Conjecture for Rankin-Selberg p-adic L-functions

2014/08/18 by Xin Wan, Wan, Xin
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1408.4044

openalex publication_date 2014/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove that the p-adic L-function that interpolates the Rankin-Selberg product of a general modular form and a CM form of higher weight divides the characteristic ideal of the corresponding Selmer group. This is one divisibility of the Iwasawa main conjecture for the p-adic L-function. We prove this conjecture using the congruences between Klingen Eisensteinseries and cusp forms on the group GU(3; 1), following the strategy of a recent work of C. Skinner and E. Urban. This theorem can be used to deduce a converse of Gross-Zagier-Kolyvagin theorem and the precise BSD formula in the rank one case.

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