论文标题
正式德林菲尔德模块的明确互惠法
Explicit Reciprocity Laws for Formal Drinfeld Modules
论文作者
论文摘要
在本文中，我们证明了一类正式的德林菲尔德模块的显式互惠法，本着特征零的精神的精神，具有稳定的高度降低（参见威尔斯的工作）。我们首先用在积极特征的本地领域定义的正式Drinfeld模块的语言定义Kummer配对。然后，我们根据正式的Drinfeld模块的对数，某个Coleman Power系列，扭转点和痕迹证明了这种配对的明确公式。我们的结果扩展了Anglès为Carlitz模块所证明的明确公式，以及Bars and Longhi的标志标准级秩一个Drinfeld模块。遵循的方法类似于前面提到的论文中所遵循的方法，考虑到正式的德林菲尔德模块是正式的幂序列，而不再是多项式的事实。
In this paper, we prove explicit reciprocity laws for a class of formal Drinfeld modules having stable reduction of height one, in the spirit of those existing in characteristic zero (cf. the work of Wiles). We begin by defining the Kummer pairing in the language of formal Drinfeld modules defined over local fields of positive characteristic. We then prove explicit formulas for this pairing in terms of the logarithm of the formal Drinfeld module, a certain Coleman power series, torsion points and the trace. Our results extend the explicit formulas already proved by Anglès for Carlitz modules, and by Bars and Longhi for sign-normalized rank one Drinfeld modules. The approach followed is similar to the ones followed in the previously mentioned papers, taking into account the subtleties derived from the fact that the formal Drinfeld modules considered are formal power series, and are no longer polynomials.
