论文标题
对于模块化形式的显式互惠法和硫泽理论
Explicit reciprocity laws and Iwasawa theory for modular forms
论文作者
论文摘要
我们证明，特征形式$ f $的mazur-tate元素沿Cyclotomic $ \ Mathbb z_p $ extension沿相应双Selmer组的拟合理想内部（直至单个常数比例）。我们的方法始于建造通过$ p $ - 美国本地兰兰兹信件构建的本地共同体学课程。从这些类别中，我们构建了Mazur-Tate元素的代数类似物，我们直接验证了适当的拟合理想。使用Kato的Euler系统和明确的互惠法，我们证明这些代数元素将相应的Mazur-Tate元素分开，这意味着我们的定理。
We prove that the Mazur-Tate elements of an eigenform $f$ sit inside the Fitting ideals of the corresponding dual Selmer groups along the cyclotomic $\mathbb Z_p$-extension (up to scaling by a single constant). Our method begins with the construction of local cohomology classes built via the $p$-adic local Langlands correspondence. From these classes, we build algebraic analogues of the Mazur-Tate elements which we directly verify sit in the appropriate Fitting ideals. Using Kato's Euler system and explicit reciprocity laws, we prove that these algebraic elements divide the corresponding Mazur-Tate elements, implying our theorem.
