Companion forms and the structure of p-adic Hecke algebras
Companion forms and the structure of p-adic Hecke algebras
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DOI：
10.1515/crll.2005.2005.585.141
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发表时间：
2004-03
期刊：
影响因子：
--
通讯作者：
M. Ohta
中科院分区：
文献类型：
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作者：
M. Ohta
摘要 我们研究了依附于模形式的 Hida 普通 p 进 Hecke 代数的爱森斯坦分量的结构，以及模形式空间 (mod p) 中的伴随形式。我们证明，如果具有伴生的模形式 (mod p) 的某个空间是一维的，则这样的代数是 Gorenstein 环；并给出这个一维性的数值标准。这与斯金纳和怀尔斯的作品部分重叠。但我们的方法基于乌尔默的著作，却完全不同。然后我们考虑上述 Gorenstein 属性的后果。我们特别讨论了与岩泽理论的联系。
Abstract We study the structure of the Eisenstein component of Hida’s ordinary p-adic Hecke algebra attached to modular forms, in connection with the companion forms in the space of modular forms (mod p). We show that such an algebra is a Gorenstein ring if certain space of modular forms (mod p) having companions is one-dimensional; and also give a numerical criterion for this one-dimensionality. This in part overlaps with a work of Skinner and Wiles; but our method, based on a work of Ulmer, is totally different. We then consider consequences of the above mentioned Gorenstein property. We especially discuss the connection with the Iwasawa theory.