Un modele semistable de la variete de Siegel de genre 3 avec structures de niveau de type \Gamma_0(p)
Abstract
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 Nlevel 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 semistable over the prime p if g>1. Using the theory of local models of RapoportZink, we construct a semistable 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 November 1998
 DOI:
 10.48550/arXiv.math/9811009
 arXiv:
 arXiv:math/9811009
 Bibcode:
 1998math.....11009G
 Keywords:

 Mathematics  Algebraic Geometry;
 14G35 (primary) 11G18;
 14M15 (secondary)
 EPrint:
 24 pages, plain TeX