On the Bloch-Kato conjecture for elliptic modular forms of square-free level
On the Bloch-Kato conjecture for elliptic modular forms of square-free level
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DOI：
10.1007/s00209-013-1226-x
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发表时间：
2014-04-01
影响因子：
0.8
通讯作者：
Brown, Jim
中科院分区：
文献类型：
--
作者：
Agarwal, Mahesh;Brown, Jim
设为一个偶数，一个奇无平方整数，一个新形式。我们证明了在一些合理的假设下，布洛赫-加托猜想的近中心临界值的-部分有一半是正确的。的代数部分的-值限定了下面相应的Bloch-Kato Selmer群的阶的-值。我们通过构造的Saito-Kurokawa举升与一个cuspidal Siegel模形式之间的同余来证明这一点。
Let be an even integer, an odd square-free integer, and a newform. We prove that under some reasonable assumptions that half of the -part of the Bloch-Kato conjecture for the near central critical value is true. We do this by bounding the -valuation of the order of the appropriate Bloch-Kato Selmer group below by the -valuation of algebraic part of . We prove this by constructing a congruence between the Saito-Kurokawa lift of and a cuspidal Siegel modular form.