AI 中文总结
该研究确定了ℂₚ的完美子域的u-不变量构成的数集，对任意特征p域的u-不变量构造出同u-不变量的完美域，证明此类u-不变量也可作为特征零域的u-不变量。
AI 中文摘要
设p≠2为素数，我们确定了作为ℂₚ的完美子域的u-不变量出现的数集。对于任何特征p域的u-不变量，我们给出了具有相同u-不变量的完美域的显式构造。特别地，若某数是特征p域的u-不变量，则它也是特征零域的u-不变量。
英文摘要
Let $p\neq 2$ be a prime. We determine the set of numbers that occur as the $u$-invariant of perfectoid subfields of $\mathbb{C}_p$. Given any number that is the $u$-invariant of a field of characteristic $p$, we give an explicit construction of a perfectoid field with the same $u$-invariant. In particular, if a number is the $u$-invariant of a field of characteristic $p$, it is also the $u$-invariant of a field of characteristic zero.
