数域K-理论局部化序列的分裂
Splitting in the K-theory localization sequence of number fields
摘要：
设p是有理数素数，F是数域.然后，对于每个i> 0，存在K_{2i}（F）的短精确定位序列。如果p是奇数或F是非例外的，我们找到了这个正合序列分裂的充要条件：这些条件涉及域F（μ_{p ^n}）的某些子域的p-类群的扭p-部分的共不变量，n是\in N.我们还比较了我们的条件与较弱的条件WK ^{et}_{2i}（F）= 0，并给出了一些例子。
英文摘要：
Let p be a rational prime and let F be a number field. Then, for each i>0, there is a short exact localization sequence for K_{2i}(F). If p is odd or F is nonexceptional, we find necessary and sufficient conditions for this exact sequence to split: these conditions involve coinvariants of twisted p-parts of the p-class groups of certain subfields of the fields F(μ_{p^n}) for n\in N. We also compare our conditions with the weaker condition WK^{et}_{2i}(F)=0 and give some example.
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