Note that both sides of this isomorphism can be regarded as locally ringed topological spaces.
---- 此同构的两端都可看作局部环拓扑空间.
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It is natural to ask whether one can compare the structure sheaves on both sides.
---- 自然要问,可否比较两端的结构 sheaves.
评论:原作没有满足于得到同胚,而是进一步提出问题(体现出“追求彻底”的思想方法)。
(我们的教授大多武断,或不允许提出此等问题,也就不会有下文了)
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There is the obvious obstacle that the left-hand side has a sheaf of characteristic p rings, wheeas the right-hand side has a sheaf of characteristic 0 rings.
---- 明显的障碍是,左端有一沓特征p环,右端则有一沓特征0环.
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Fontaine's functors make it possible to translate between the two worlds.