Return to Revisions

If the two dvrs $S$ and $T$ are torsion-free over the base dvr $R$, then $S$ and $T$ are flat over $R$. So the tensor product is flat over $S$ (and over $T$). Therefore if the tensor products of the quotient fields $Q(S)\otimes_{Q(R)}Q(T)$ is reduced, then so is $S \otimes_R T$.