论文标题
通过kummer理论的GL_2的显式塞雷重量
Explicit Serre weights for GL_2 via Kummer theory
论文作者
论文摘要
我们使用Kummer理论给出了SERRE猜想的重量部分的明确配方。这避免了对P-Adic Hodge理论的任何参考。关键输入是对晶体扩展的还原模量的描述，该模量是某些“ G_K-Artin-Scheier Cocycles”的描述，以及Abrashkin的结果，它用Kummer理论描述了这些共生。 Dembele-Diamond-Roberts先前在未受到的案例和一般的第二作者中给出了替代性的明确表述。我们表明，可以使用Brueckner-Shaferevich-Vostokov的显式互惠法直接从我们的dembele-Diamond-Roberts进行描述。这些计算说明了我们对Kummer理论的使用如何消除这两篇论文中出现的某些组合并发症。
We give an explicit formulation of the weight part of Serre's conjecture for GL_2 using Kummer theory. This avoids any reference to p-adic Hodge theory. The key inputs are a description of the reduction modulo p of crystalline extensions in terms of certain "G_K-Artin-Scheier cocycles" and a result of Abrashkin which describes these cocycles in terms of Kummer theory. An alternative explicit formulation in terms of local class field theory was previously given by Dembele-Diamond-Roberts in the unramified case and by the second author in general. We show that the description of Dembele-Diamond-Roberts can be recovered directly from ours using the explicit reciprocity laws of Brueckner-Shaferevich-Vostokov. These calculations illustrate how our use of Kummer theory eliminates certain combinatorial complications appearing in these two papers.
