Semi-stable model of the Siegel variety of genus 3 with a Γ0(p)-level structure

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 greater than or equal to3 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 integral 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.