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You cannot define the variety as the set of valuations. Birational varieties will have the same set of valuations.

As far as I am remember, logicians were looking at it for a while. If you have spare 250 bucks, you can learn something there.

show/hide this revision's text 1

You cannot define the variety as the set of valuations. Birational varieties will have the same set of valuations.

As far as I am remember, logicians were looking at it for a while. If you have spare 250 bucks, you can learn something there.