For a field $F$ (for example, a one generated by a finite number of its elements) there is a directed set of its 'models' (in this case those are 'arithmetic' schemes whose fraction field is $F$). It seems that codimension $1$ irreducible subvarieties of these models yield valuations of $F$. My question is: which valuations are obtained this way? Would it be appropriate to call them 'geometric'; is there any canonical text that treats this question (an introduces some terms of sort)? The problem is that I do not want to restrict myself to the case when all of these subschemes are defined over a fixed subfield of $F$.

For a field $F$ (for example, a one generated by a finite number of its elements) there is a directed set of its 'models' (in this case those are 'arithmetic' schemes whose fraction field is $F$). It seems that codimension $1$ irreducible subschemes of these models yield valuations of $F$. My question is: which valuations are obtained this way? Would it be appropriate to call them 'geometric'; is there any canonical text that treats this question (an introduces some terms of sort)? The problem is that I do not want to restrict myself to the case when all of these subschemes are defined over a fixed subfield of $F$.