The Iwasawa Main Conjectures for ${\rm GL}_2$ and derivatives of $p$-adic $L$-functions

Francesc Castella; Xin Wan

The Iwasawa Main Conjectures for ${\rm GL}_2$ and derivatives of $p$-adic $L$-functions

Number Theory 2020-01-14 v1

Authors: Francesc Castella , Xin Wan

Abstract

We prove under mild hypotheses the three-variable Iwasawa main conjecture for $p$ -ordinary modular forms in the indefinite setting. Our result is in a setting complementary to that in the work of Skinner-Urban, and it has applications to Greenberg's nonvanishing conjecture for the first derivatives at the center of $p$ -adic $L$ -functions of cusp forms in Hida families with root number $-1$ and to Howard's horizontal nonvanishing conjecture.

Keywords

iwasawa main conjecture gl_2 p-adic l-functions modular forms hida families nonvanishing conjecture

Cite

@article{arxiv.2001.03878,
  title  = {The Iwasawa Main Conjectures for ${\rm GL}_2$ and derivatives of $p$-adic $L$-functions},
  author = {Francesc Castella and Xin Wan},
  journal= {arXiv preprint arXiv:2001.03878},
  year   = {2020}
}

Comments

33 pages

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