Un modele semi-stable 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 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.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- November 1998
- DOI:
- 10.48550/arXiv.math/9811009
- arXiv:
- arXiv:math/9811009
- Bibcode:
- 1998math.....11009G
- Keywords:
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- Mathematics - Algebraic Geometry;
- 14G35 (primary) 11G18;
- 14M15 (secondary)
- E-Print:
- 24 pages, plain TeX