On Serre?s conjecture over imaginary quadratic fields

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• 作者：Rebecca Torrey¹ ; ^{rtorrey@amherst.edu}
• 关键词：Serre?s conjecture ; Hecke operator ; Galois representation ; Modular form
• 刊名：Journal of Number Theory
• 出版年：2012
• 出版时间：April 2012
• 年：2012
• 卷：132
• 期：4
• 页码：637-656
• 全文大小：242 K

文摘

We study an analog of Serre?s conjecture over imaginary quadratic fields. In particular, we ask whether the weight recipe of Buzzard, Diamond and Jarvis will hold in this setting. Using a program written by the author, we provide computational evidence that this is in fact the case. In order to justify the method used in the program, we prove that a modular symbols method will work for arbitrary weights over imaginary quadratic fields.