Refined applications of Kato's Euler systems for modular forms
Number Theory
2023-11-22 v4
Abstract
We discuss refined applications of Kato's Euler systems for modular forms of higher weight at good primes (with more emphasis on the non-ordinary ones) beyond the one-sided divisibility of the main conjecture and the finiteness of Selmer groups. These include a proof of the Mazur--Tate conjecture on Fitting ideals of Selmer groups over -cyclotomic extensions and a new interpretation of the Iwasawa main conjecture via the non-triviality of Kato's Kolyvagin systems with structural applications. Some applications to Birch and Swinnerton-Dyer conjecture are also discussed.
Cite
@article{arxiv.2203.12157,
title = {Refined applications of Kato's Euler systems for modular forms},
author = {Chan-Ho Kim},
journal= {arXiv preprint arXiv:2203.12157},
year = {2023}
}
Comments
The period convention is now written more clearly. Proposition 8.8 and the related parts are corrected. Comments welcome