Putman, Andrew2013-09-132013-09-132012Putman, Andrew. "The Picard group of the moduli space of curves with level structures." <i>Duke Mathematical Journal,</i> 161, no. 4 (2012) 623-674. http://dx.doi.org/10.1215/00127094-1548362.https://hdl.handle.net/1911/71892For 4 - L and g large, we calculate the integral Picard groups of the moduli spaces of curves and principally polarized abelian varieties with level L structures. In particular, we determine the divisibility properties of the standard line bundles over these moduli spaces and we calculate the second integral cohomology group of the level L subgroup of the mapping class group (in a previous paper, the author determined this rationally). This entails calculating the abelianization of the level L subgroup of the mapping class group, generalizing previous results of Perron, Sato, and the author. Finally, along the way we calculate the first homology group of the mod L symplectic group with coefficients in the adjoint representation.engThis is an author’s peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Duke University Press.Journal articlehttp://dx.doi.org/10.1215/00127094-1548362DMS-1005318 (National Science Foundation)