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Denote the complement of the discriminant locus by $B_0 = B \\setminus \\operatorname{Disc}(\\pi)$, its preimage by $X_0 = \\pi^{-1}(B_0)$, and the complement of the critical locus by $X' = X \\setminus \\operatorname{Sing}(\\pi)$. Under an assumption that the morphism $X' \\to B$ is surjective, we construct (1) the N\\'eron model of the abelian fibration $\\pi_0 : X_0 \\to B_0$ and (2) the N\\'eron model of its automorphism abelian scheme $\\operatorname{Aut}^{\\circ}_{\\pi_0} \\to B_0$. 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Denote the complement of the discriminant locus by $B_0 = B \\setminus \\operatorname{Disc}(\\pi)$, its preimage by $X_0 = \\pi^{-1}(B_0)$, and the complement of the critical locus by $X' = X \\setminus \\operatorname{Sing}(\\pi)$. Under an assumption that the morphism $X' \\to B$ is surjective, we construct (1) the N\\'eron model of the abelian fibration $\\pi_0 : X_0 \\to B_0$ and (2) the N\\'eron model of its automorphism abelian scheme $\\operatorname{Aut}^{\\circ}_{\\pi_0} \\to B_0$. 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