论文标题
CM字段上的自动形态galois表示的刚度
Rigidity of Automorphic Galois Representations over CM Fields
论文作者
论文摘要
我们显示了CM领域上伴随的自动形态galois表示的伴奏Bloch-kato Selmer群的消失。这证明了它们的刚性，因为它们没有De Rham的变形。为了使这一点有道理，我们还证明了CM领域上的自动形态Galois表示是De Rham本身。我们的方法大量从10篇作者论文中获取，在那里对这些Galois表示进行了广泛的研究。另一个至关重要的灵感来自P. Allen的工作，P。Allen使用了特征0中某些局部变形环的平滑度来在极化情况下获得刚性。
We show the vanishing of adjoint Bloch-Kato Selmer groups of automorphic Galois representations over CM fields. This proves their rigidity in the sense that they have no deformations which are de Rham. In order for this to make sense we also prove that automorphic Galois representations over CM fields are de Rham themselves. Our methods draw heavily from the 10 author paper, where these Galois representations were studied extensively. Another crucial piece of inspiration comes from the work of P. Allen who used the smoothness of certain local deformation rings in characteristic 0 to obtain rigidity in the polarized case.
