The Eisenstein ideal with squarefree level
The Eisenstein ideal with squarefree level
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DOI：
10.1016/j.aim.2020.107543
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发表时间：
2018-04
影响因子：
1.7
通讯作者：
Preston Wake;Carl Wang-Erickson
中科院分区：
文献类型：
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作者：
Preston Wake;Carl Wang-Erickson
本文利用伪表象的变形理论研究了Mazur的Eisenstein理想在无平方能级上的模拟。给定素数p> 3和满足一定条件的无平方数N，研究了p-adic Hecke代数的Eisenstein部分，证明了它是一个局部完全交且同构于一个伪变形环.我们还表明，在某些情况下，爱森斯坦理想不是主要的，尖点商的Hecke代数不是Gorenstein。作为推论，我们证明了在这些情况下，“重数1”对于模雅可比矩阵J 0（N）是不成立的。在一个特殊的情况下，这证明了一个猜想Ribet。
We use deformation theory of pseudorepresentations to study the analogue of Mazur's Eisenstein ideal with squarefree level. Given a prime number p> 3 and a squarefree number N satisfying certain conditions, we study the Eisenstein part of the p-adic Hecke algebra for Γ 0 (N), and show that it is a local complete intersection and isomorphic to a pseudodeformation ring. We also show that, in certain cases, the Eisenstein ideal is not principal and that the cuspidal quotient of the Hecke algebra is not Gorenstein. As a corollary, we prove that “multiplicity one” fails for the modular Jacobian J 0 (N) in these cases. In a particular case, this proves a conjecture of Ribet.