Tame ramification of normal schemes

In the remaining part of 5 2 we make the following assumptions and notations S is a locally noetherian, normal scheme, D is a closed subset of S of codimension at least one and 

3) every irreducible component of X dominates an irreducible component of S, 

Remarks 1) The use of the word covering is somewhat misleading (like the translation of revetement Stale into Stale covering ), namely f is not necessarily surjective if S is not connected. 

2) As to the terminology instead of tamely ramified covering of S relative to D we use also covering of S tamely ramified over D , or short X tame over S relative to D , or X tame over S if there is no confusion about D. 

Consider the total ring of quotients of B. By condition 2) this is 

Note that for s S of codimension one (i.e., dim Og = 1) the local ring Og g is a discrete valuation ring. Finally, if X is a scheme then R(X) denotes the ftmction ring of X in the sense of EGA I 7 1 2, 

---