Semistable reduction for overconvergent F-isocrystals, II: A valuation-theoretic approach
Semistable reduction for overconvergent F-isocrystals, II: A valuation-theoretic approach
复制标题
过收敛 F-等晶的半稳定还原，II：评估理论方法
作者：
K. Kedlaya
摘要我们引入了一种赋值理论方法来研究具有Frobenius结构的过收敛同晶的半稳定约化问题（即在适当的覆盖上存在对数扩张）。关键的工具是与一个簇的函数域相关联的黎曼-Zerkki空间的拟紧性。我们还做了一些初始的简化，这使得我们可以将注意力集中在高度为1和超越度为0的估值上。
Abstract We introduce a valuation-theoretic approach to the problem of semistable reduction (i.e. existence of logarithmic extensions on suitable covers) of overconvergent isocrystals with Frobenius structure. The key tool is the quasicompactness of the Riemann–Zariski space associated to the function field of a variety. We also make some initial reductions, which allow attention to be focused on valuations of height 1 and transcendence degree 0.