# Aggressive geometry – Flattening and dualizing template of a family of curves

I'm trying to see if the following things are valid: a family of curves $$pi: X rightarrow S$$ or $$pi$$ is clean and flat and diets $$X$$ and $$S$$ are arbitrary is it true that the sheaf of relative splitting exists? In addition, I would like to know if you are considering a vector bundle $$E$$ sure $$X$$ and flat $$S$$, the tensor product of $$E$$ with the sheaf in relative duel is flat. Thank you for your time.