On Serre's conjecture for 2-dimensional mod p representations of Gal( Q=Q)
On Serre's conjecture for 2-dimensional mod p representations of Gal( Q=Q)
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关于 Gal( Q=Q) 的二维 mod p 表示的 Serre 猜想
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
J.
中科院分区：
文献类型：
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作者：
C. Khare;J.
我们证明了在许多情况下存在的极小分歧的p-adic升降机的2维连续，奇数，绝对不可约，模p表示的绝对伽罗瓦群Q。据预测塞尔的猜想，这种表示产生于新形式的最佳水平和重量。使用这些最小的升降机，并使用兼容系统的参数，我们证明了一些情况下塞尔的apturtures在低水平和重量。例如，我们证明了Z上不存在不可约（p;p）型群概型.我们证明了上述的Artin导体1和Serre权12的a来自Ramanujan Delta函数。在本文的最后一部分，我们提出的论点，减少塞尔的猜想证明推广的模块化提升定理的类型开创了怀尔斯。
We prove the existence in many cases of minimally ramied p-adic lifts of 2-dimensional continuous, odd, absolutely irreducible, mod p representations of the absolute Galois group of Q. It is predicted by Serre’s conjecture that such representations arise from newforms of optimal level and weight. Using these minimal lifts, and arguments using compatible systems, we prove some cases of Serre’s conjectures in low levels and weights. For instance we prove that there are no irreducible (p;p) type group schemes over Z. We prove that a as above of Artin conductor 1 and Serre weight 12 arises from the Ramanujan Delta-function. In the last part of the paper we present arguments that reduce Serre’s conjecture to proving generalisations of modularity lifting theorems of the type pioneered by Wiles.