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We discuss refined applications of Kato's Euler systems for modular forms ofhigher weight at good primes (with more emphasis on the non-ordinary ones)beyond the one-sided divisibility of the main conjecture and the finiteness ofSelmer groups. These include a proof of the Mazur--Tate conjecture on Fittingideals of Selmer groups over $p$-cyclotomic extensions and a new interpretationof the Iwasawa main conjecture via the non-triviality of Kato's Kolyvaginsystems with structural applications. Some applications to Birch andSwinnerton-Dyer conjecture are also discussed.

Refined applications of Kato's Euler systems for modular forms