论文标题
Kato的Euler Systems用于模块化形式的精制应用
Refined applications of Kato's Euler systems for modular forms
论文作者
论文摘要
我们讨论了Kato的Euler Systems的精致应用，以超出主要猜想的单方面分裂性和Selmer群体的有限性，以良好的素数（更加重视非平常）的模块化形式。其中包括对$ p $ cyclotomic扩展的安装理想的Mazur-Tate猜想，以及通过Kato的Kato Kato的Kolyvagin Systems具有结构应用的非平地性的iWasawa Main猜想的新解释。还讨论了对桦木和Swinnerton-Dyer猜想的一些应用。
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.
