Let $C$ be a curve (smooth projective over a field k) and $p$ a rational point on $C$. Put $\dot{C}=C\{p\}$. Set $T=Spec R$ where $R$ is a noetherian kalgebra. Let $Y$ be a locally trivial fiber bundle (suppose for etale topology), with smooth affine fibers, over $\dot{C}_T:=\dot{C}\times T$. My question is as follows: can one extend the fiber bundle Y to a flat family over entire relative curve $C_T$?
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