  Let S(g,N,p) be the Siegel modular variety of principally polarized abelian
varieties of dimension g with a \Gamma_0(p)-level structure and a full N-level
structure (where p is a prime not dividing N \geq 3 and \Gamma_0(p) is the
inverse image of a Borel subgroup of Sp(2g,F_p) in Sp(2g,Z)). This variety has
a natural integral model over Z[1/N] which is not semi-stable over the prime p
if g>1.
  Using the theory of local models of Rapoport-Zink, we construct a semi-stable
model of S(g,N,p) over Z[1/N] for g=2 and g=3.
  For g=2, our construction differs from de Jong's one though the resulting
model is the same.

Algebraic Geometry