We compute the Picard group of the universal Abelian variety over the moduli stack of principally polarized Abelian varieties over with a symplectic principal level -structure. We then prove that over the statement of the Franchetta conjecture holds in a suitable form for .
"The Picard Group of the Universal Abelian Variety and the Franchetta Conjecture for Abelian Varieties." Michigan Math. J. 68 (3) 651 - 671, August 2019. https://doi.org/10.1307/mmj/1564106669