  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.
