Iwasawa Main Conjecture for Rankin-Selberg $p$-adic $L$-functions: Non-Ordinary Case

Xin Wan

Iwasawa Main Conjecture for Rankin-Selberg $p$-adic $L$-functions: Non-Ordinary Case

Number Theory 2021-09-21 v3

Authors: Xin Wan

Abstract

In this paper we prove that the $p$ -adic $L$ -function that interpolates the Rankin-Selberg product of a general weight two modular form which is unramified and non-ordinary at $p$ , and an ordinary CM form of higher weight contains the characteristic ideal of the corresponding Selmer group. This is one divisibility of the Iwasawa-Greenberg main conjecture for the $p$ -adic $L$ -function. This generalizes an earlier work of the author to the non-ordinary case. The result of this paper plays a crucial role in the proof of Iwasawa main conjecture and refined Birch-Swinnerton-Dyer formula for supersingular elliptic curves.

Keywords

Iwasawa main conjecture Rankin-Selberg $p$-adic $L$-functions non-ordinary case Selmer group modular forms CM forms supersingular elliptic curves Birch-Swinnerton-Dyer formula

Cite

@article{arxiv.1412.1767,
  title  = {Iwasawa Main Conjecture for Rankin-Selberg $p$-adic $L$-functions: Non-Ordinary Case},
  author = {Xin Wan},
  journal= {arXiv preprint arXiv:1412.1767},
  year   = {2021}
}

Comments

It is completely re-written by the author with Francesc Castella and Zheng Liu as a collaboration, as arXiv:2109.08375

Iwasawa Main Conjecture for Rankin-Selberg $p$-adic $L$-functions: Non-Ordinary Case

Abstract

Keywords

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