论文标题
Super-Hölder向量和规范领域
Super-Hölder vectors and the field of norms
论文作者
论文摘要
令E为特征p的领域。在我们的先前论文中，我们在z_p的某些电子线性表示中定义和研究了Super-Hölder向量。在本文中，我们在一般P-Adic Lie组的某些E线性表示中定义和研究Super-Hölder载体。然后，我们考虑P-Adic场K的某些P-Adic Lie Extensions K_ \ Infty / K，并计算K_ \ Infty倾斜的Super-Hölder矢量。 We show that these super-Hölder vectors are the perfection of the field of norms of K_\infty / K. By specializing to the case of a Lubin-Tate extension, we are able to recover E((Y)) inside the Y-adic completion of its perfection, seen as a valued E-vector space endowed with the action of O_K^\times given by the endomorphisms of the corresponding Lubin-Tate group.
Let E be a field of characteristic p. In a previous paper of ours, we defined and studied super-Hölder vectors in certain E-linear representations of Z_p. In the present paper, we define and study super-Hölder vectors in certain E-linear representations of a general p-adic Lie group. We then consider certain p-adic Lie extensions K_\infty / K of a p-adic field K, and compute the super-Hölder vectors in the tilt of K_\infty. We show that these super-Hölder vectors are the perfection of the field of norms of K_\infty / K. By specializing to the case of a Lubin-Tate extension, we are able to recover E((Y)) inside the Y-adic completion of its perfection, seen as a valued E-vector space endowed with the action of O_K^\times given by the endomorphisms of the corresponding Lubin-Tate group.
