附加循环惯量的线性系
Linear systems attached to cyclic inertia
摘要：
本文归纳地构造了特征$p>0$域上有限长Witt向量代数群${\mathbb W}_n$的等变紧化.我们得到了光滑的射影有理簇$\bar{\mathbb W}_n$，定义在$\mathbf F_p$上，边界是一个约数，其约化的子方案具有正常的交叉。Artin-Schreier-Witt等价的$F-1:{\mathbb W}_n\to {\mathbb W}_n$扩张到一个有限的循环覆盖${\mathbfΨ}_n:\bar{\mathbb W}_n\to \bar{\mathbb W}_n$，其度为$p^n$，在边界处分支.这是用来给一个外在的描述的局部行为的可分离覆盖的曲线在字符。$p$在惯性群为循环的广分歧点处的解。在附录中，我们给出了这种覆盖的导体的初等计算，否则可以使用类域理论来确定。
英文摘要：
We construct inductively an equivariant compactification of the algebraic group ${\mathbb W}_n$ of Witt vectors of finite length over a field of characteristic $p>0$. We obtain smooth projective rational varieties $\bar{\mathbb W}_n$, defined over $\mathbf F_p$; the boundary is a divisor whose reduced subscheme has normal crossings. The Artin-Schreier-Witt isogeny $F-1:{\mathbb W}_n\to {\mathbb W}_n$ extends to a finite cyclic cover ${\mathbfΨ}_n:\bar{\mathbb W}_n\to \bar{\mathbb W}_n$ of degree $p^n$ ramified at the boundary. This is used to give an extrinsic description of the local behavior of a separable cover of curves in char. $p$ at a wildly ramified point whose inertia group is cyclic. In an appendix, we give an elementary computation of the conductor of such a covering, which can otherwise be determined using class field theory.
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