论文标题
Eisenstein适合重量K和适应家庭的Bloch-Kato猜想
The Eisenstein ideal for weight k and a Bloch-Kato conjecture for tame families
论文作者
论文摘要
我们研究Eisenstein的模块化形式的理想，即重量$ k> 2 $和Prime Level Level $ n $。我们特别注意$ \ mathit {extra \ delucibility} $的现象：Eisenstein Ideal严格比理想的削减可简化的Galois表示形式大。我们证明了这些额外的还原表示的模块化定理。结果，我们将Mazur-Tate $ L $功能的衍生物与Hecke代数的等级联系起来，概括了Merel的定理，并提供了一个新的Kato主要猜想的特殊案例。在本文的后半部分，我们回想起卡托对这一主要猜想的表述，如果指示器$ n $和$ n $和$ p $ - 权力订单的曲折及其与Equivariant主要猜想的其他配方的关系。
We study the Eisenstein ideal for modular forms of even weight $k>2$ and prime level $N$. We pay special attention to the phenomenon of $\mathit{extra \ reducibility}$: the Eisenstein ideal is strictly larger than the ideal cutting out reducible Galois representations. We prove a modularity theorem for these extra reducible representations. As consequences, we relate the derivative of a Mazur-Tate $L$-function to the rank of the Hecke algebra, generalizing a theorem of Merel, and give a new proof of a special case of an equivariant main conjecture of Kato. In the second half of the paper, we recall Kato's formulation of this main conjecture in the case of a family of motives given by twists by characters of conductor $N$ and $p$-power order and its relation to other formulations of the equivariant main conjecture.
