Cohomological vanishing on Siegel modular varieties and applications to   lifting Siegel modular forms
  We use vanishing results for sheaf cohomology on Siegel modular varieties to study two lifting problems:   (a) When can Siegel modular forms (mod p) be lifted to characteristic zero? This uses and extends previous results for cusp forms by Stroh and Lan-Suh.   (b) When is the restriction of Siegel modular forms to the boundary of the moduli space a surjective map? We investigate this question in arbitrary characteristic, generalising analytic results of Weissauer and Arakawa. 
Alexandru Ghitza and Scott Mullane
math.NT math.AG