Normal crossings on a surface and ordinary double points Let $R$ be a discrete valuation ring with residue field $F$, and let $X/R$ be a regular projective relative curve with closed fiber $X_0$.  Then $X_0/F$ is a projective curve.  We know that $X$ may be transformed by blow-up into a regular proj. rel. curve for which $X_0$ has normal crossings.  As I understand it, the reduced structure $C=(X_0)_{red}$ has regular irreducible components, at most two of which meet at any point, and when they meet, they meet transversally.  My questions: (1) are the singular points of $C$ necessarily ordinary double points?  (2) If not, does the answer change if $F$ is perfect?  I'm not an algebraic/arithmetic geometer, and I'm trying to read a paper by Saito (Class field theory for curves over local fields, JNT 21 (1985), 44-80).  Thank you in advance for any comments/references.
EricB
 A: For the question (1), it depends on the definition of ordinary double point. If you use that of Deligne-Mumford or Bosch-Lütkebohmert-Raynaud ($C$ at the singular point is isomorphic to $\mathrm{Spec}(F[x,y]/(xy))$ for the étale topology) then it implies that the residue field at the singular point is separable over $F$. In general embedded resolution of singularities gives you regular (not necessary smooth) irreducible component, and the residue field at the singular points of $C$ may be inseparable over $F$, even when the generic fiber is smooth over $\mathrm{Frac}(R)$. 
Example: take $R=F[[t]]$ and use a local equation $y^2=x^p-\lambda+tx$ with $p=\mathrm{char}(F)>0$ and $\lambda\in F$ is not a $p$-th power in $F$. You get an irreducible component which is regular but not smooth. Then you can blow-up as many times as you want, the stricit transform of this component will be finite and birational (hence isomorphic) to the initial one, so you never get a smooth component. Similar constructions can be done for singular points in $C$. If you have  a singular point in $C$ with inseparable residue field, then blowing-up this point still gives inseparable points. 
(2) If $F$ is perfect, then yes, everything agree. 
A: Normal crossing singularities of a reduced curve are ordinary double points by definition. 
If you allow base change, then you can even ask that $X_0$ be reduced.
A: That would be great, and thanks for the quick reply.  Let me make sure I understand:  Say $X_0$ is reduced, and $x$ is a singular point.  The definition I have for normal crossings would say that $X_0$ would be cut out at $x$ by a regular system of parameters $\{f,g\}$ for the local ring $O_{X,x}$.  If $x$ is an ordinary double point for $X_0/F$, then (by the definition I have) the completion at $x$ looks like $F[[\bar f,\bar g]]/(\bar f\bar g)$.  How do you get from one to the other?  For example if a uniformizer $t$ for $R$ is not prime in $O_{X,x}$, the structure theorem for complete regular local rings is not very explicit.
I thought it was an interesting question because the normal crossings definition seems to rely on the ambient scheme, whereas "double point" seems more intrinsic to the curve.  
EricB
