On the syntomic regulator for K1 of a surface
On the syntomic regulator for K1 of a surface
复制标题
曲面 K1 的语义调节器
DOI：
10.1007/s11856-011-0188-0
复制
发表时间：
2012
影响因子：
1
通讯作者：
Amnon Besser
中科院分区：
文献类型：
--
作者：
Amnon Besser
我们考虑K_1（S）的元素，其中S是p-adic域上具有良好约化的真曲面，这些元素由形式和给出，其中Z_i曲线在S中，fi是Z_i上的有理函数，使得fi的因子之和在S上为0.假设向前推进在同分和动机上同调中的相容性，我们的结果计算了这样一个元素的同分调节器，当由第二类形式η的第一上同调类在全纯形式ω的杯积ω [η]上求值时，该元素被解释为HdR 2（S）上的泛函。结果是<$i <$Fη，log（fi）; Fω <$gl，Zi，其中Fω和Fη分别是ω和η的科尔曼积分，括号中的符号是整体三重指标，如我们以前的工作中定义的。
We consider elements of K1(S), where S is a proper surface over a p-adic field with good reduction, which are given by a formal sum Σ(Zi, fi) with Zi curves in S and fi rational functions on the Zi in such a way that the sum of the divisors of the fi is 0 on S. Assuming compatibility of pushforwards in syntomic and motivic cohomologies, our result computes the syntomic regulator of such an element, interpreted as a functional on HdR2(S), when evaluated on the cup product ω∪[η] of a holomorphic form ω by the first cohomology class of a form of the second kind η. The result is Σi〈Fη, log(fi); Fω〉gl,Zi, where Fω and Fη are Coleman integrals of ω and η, respectively, and the symbol in brackets is the global triple index, as defined in our previous work.