论文标题
阳性特征中环形完美素场的重新完成
Decompletion of cyclotomic perfectoid fields in positive characteristic
论文作者
论文摘要
令$ e $为特征$ p $的字段。组$ \ mathbf {z} _p^\ times $在$ e（（x））$ by $ a \ cdot f（x）= f（（（1+x）^a-1）$上。此操作延伸到$ x $ -Adic完成$ \ tilde {\ Mathbf {e}} $ $ \ cup_ {n \ geq 0} e（（（x^{1/p^n}）））$。我们展示了如何从价值$ e $ -e $ -vector Space $ \ tilde {\ Mathbf {e}} $中恢复$ e（（x））$，并赋予其$ \ mathbf {z} _p^\ times $的操作。为此，我们在$ \ mathbf {z} _p $的某些$ e $ linear表示中介绍了Super-Höldervector的概念。这是本地分析矢量概念的特征性$ p $类似物，以$ p $ p $ - adic-adic Lie Groups的$ p $ -ADIC BANACH表示。
Let $E$ be a field of characteristic $p$. The group $\mathbf{Z}_p^\times$ acts on $E((X))$ by $a \cdot f(X) = f((1+X)^a-1)$. This action extends to the $X$-adic completion $\tilde{\mathbf{E}}$ of $\cup_{n \geq 0} E((X^{1/p^n}))$. We show how to recover $E((X))$ from the valued $E$-vector space $\tilde{\mathbf{E}}$ endowed with its action of $\mathbf{Z}_p^\times$. To do this, we introduce the notion of super-Hölder vector in certain $E$-linear representations of $\mathbf{Z}_p$. This is a characteristic $p$ analogue of the notion of locally analytic vector in $p$-adic Banach representations of $p$-adic Lie groups.
