The top Chern class of the Hodge bundle on the moduli space of abelian   varieties
  We give upper and lower bounds for the order of the top Chern class of the Hodge bundle on the moduli space of principally polarized abelian varieties. We also give a generalization to higher genera of the famous formula $12 \lambda_1=\delta$ for genus 1. 
Torsten Ekedahl and Gerard van der Geer