2019-4-24 14:12

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Claim 1.4. The affine line A&sup1;K `is equal to' the inverse limit lim<A&sup1;K (TT), where T is the coordinate on A&sup1;.

---- 给出了两个对象 A&sup1;K 和 lim<A&sup1;K (TT) “相等” 的断言.

(可能是指等价或同构).

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One way in which this is correct is the observation that it is true on K-, resp. K-, valued points.

---- 断言在相应的取值点上正确.

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Moreover, for any finite extension L of K corresponding to an extension L of K, we have the same relation L = lim<L (x x).

---- 给出了两个完域的扩张之间的关系.

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Looking at the example above, we see that the explicit description of the map between A&sup1;K and lim<A&sup1;K (TT) involves a limit procedure.

---- 注意到 A&sup1;K 和 lim<A&sup1;K (TT) 之间的映射涉及到一个极限过程.

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For this reason, a formalization of this isomorphism has to be of an analytic nature, and we have to use some kind of rigid-analytic geometry over K.

---- 出于这个理由，此同构的形式化必须是解析性质的，从而不得不使用某种K上严格解析的几何.

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We choose to work with Huber's language of adic spaces, which reinterprets rigid-analytic varieties as certain locally ringed topological spaces.

---- 这里选择 adic 空间的 Huber 语言，它将严格解析簇重新阐释为某种局部环拓扑空间.

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In particular, any variety X over K has an associated adic space Xᵃᵈ over K, which in turn has an underlying topological space |Xᵃᵈ|.

---- K上的任何簇 X 都关联着一个K上的 adic 空间 Xᵃᵈ，后者有一个底层的拓扑空间 |Xᵃᵈ|.

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{​K} {K}，此处已经是完域.

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---- K°/p  K°/p.(para.3a)

---- K = lim<K, x x^p.(para.3b)

----  (x)d --> (x#)d

↑  分裂域   ↓

[K] ~>  [K]c

---- ndv(1)~K~(Φ)=K/p.

---- K(p)~Fontaine~K.