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.][1]


  [1]: http://www.amazon.com/Multi-Valued-Fields-Siberian-School-Algebra/dp/0306110687/ref=sr_1_1?s=books&ie=UTF8&qid=1279744611&sr=1-1#_