# Trivialization of a fibration after a base change

Let $E\to B$ be a locally trivial fibration of curves of genus >1 (everyhting is compact and over $\mathbb{C}$). I read that this fibration becomes trivial "after a finite unramified base change". Could anyone explain what does it mean, i.e. what is the exact construction?

• It becomes trivial after you perform a base change by the finite cover of symplectic bases for the $3$-torsion of your Abelian scheme. – Jason Starr Apr 14 '17 at 11:22
• You glue such a bundle together by transition maps: automorphisms of the fiber. But the automorphism group is finite. So after a suitable cover, you are gluing together by the identity automorphism. – Ben McKay Apr 16 '17 at 11:53