An analogue of Serre's conjecture for Galois representations and Hecke eigenclasses in the mod p$ co
An analogue of Serre's conjecture for Galois representations and Hecke eigenclasses in the mod p$ co
复制标题
mod p$ co 中伽罗瓦表示和赫克本征类的塞尔猜想的类似物
DOI：
10.1215/s0012-7094-00-10511-x
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发表时间：
1999
影响因子：
2.5
通讯作者：
W. Sinnott
中科院分区：
文献类型：
--
作者：
A. Ash;W. Sinnott
文中提到的Serre的猜想是关于奇伽罗瓦表示成GL（2，F）的模性的猜想，其中F是特征为p的有限域。我们给出了一个类似的猜想，其中GL(2)被GL(n)代替。我们解释“奇怪”的类似物。然后，我们提出了一些理论和实验证据，主要是当n = 3时。我们的猜想并不要求伽罗瓦表示不可约。我们最有趣的例子涉及不可约的偶数二维表示和一维表示的和。
The conjecture of Serre referred in the title is the one about modularity of odd Galois representations into GL(2,F) where F is a finite field of characteristic p. We present an analogous conjecture where GL(2) is replaced by GL(n). We explain the analogue of "oddness." We then present some theoretical and experimental evidence for the conjecture, primarily when n = 3. Our conjecture does not require the Galois representation to be irreducible. Our most interesting examples involve the sum of an irreducible even 2-dimensional representation and a 1-dimensional representation.