The Picard group of the universal abelian variety and the Franchetta   conjecture for abelian varieties
  We compute the Picard group of the universal abelian variety over the moduli stack $\mathscr A_{g,n}$ of principally polarized abelian varieties over $\mathbb{C}$ with a symplectic principal level $n$-structure. We then prove that over $\mathbb{C}$ the statement of the Franchetta conjecture holds in a suitable form for $\mathscr A_{g,n}$. 
Roberto Fringuelli and Roberto Pirisi
math.AG