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arXiv · 1408.4044

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

Xin Wan
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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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Xin Wan. 2014-08-18. Iwasawa Main Conjecture for Rankin-Selberg p-adic L-functions. https://arxiv.org/abs/1408.4044

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