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Jul 22, 2018 at 22:15 comment added S. Carnahan @Qfwfq The generic point corresponds to the prime $(0)$, which normally corresponds to the trivial absolute value $|x|_0 = 1-\delta_{x,0}$. On the other hand, the preimage of the generic point along the canonical map from the Berkovich spectrum contains everything except the endpoints $|-|_p^\infty$.
Jul 22, 2018 at 20:50 comment added Qfwfq I just came across this post now - maybe someone around or the OP himself may still answer though :-) "Z has a valuation that is not captured by the points of the topological space, namely the usual Archimedean absolute value" - I have a naive question: isn't the generic point of SpecZ meant to correspond to the Archimedean absolute value on Z?
Nov 23, 2009 at 15:20 vote accept Abtan Massini
Nov 22, 2009 at 1:17 history answered S. Carnahan CC BY-SA 2.5