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arXiv · 2203.12157

Refined applications of Kato's Euler systems for modular forms

Chan-Ho Kim
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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 $p$-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.

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Chan-Ho Kim. 2022-03-23. Refined applications of Kato's Euler systems for modular forms. https://arxiv.org/abs/2203.12157

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