Geodesic
Foliations in moduli spaces of abelian varieties
Oort, Frans1
1Mathematisch Instituut, Postbus 80.010, NL-3508 TA Utrecht, The Netherlands
Journal of the American Mathematical Society, Tome 17 (2004) no. 2, pp. 267-296

Voir la notice de l'article provenant de la source American Mathematical Society

We study moduli spaces of polarized abelian varieties in positive characteristic. Our final goal will be to understand Hecke orbits in such spaces. This paper provides one of the tools. For a given $p$-divisible group, all abelian varieties which give rise to this group have moduli points in a locally closed subset of the moduli space; we call an irreducible component of this subset a central leaf. Newton polygon strata are foliated by such leaves. Moreover, iterated $\alpha _p$-isogenies give a second leaf structure, which was already known under the name of Rapoport-Zink spaces. Any Newton polygon stratum is, up to a finite morphism, isomorphic to a product of an isogeny leaf and a finite cover of a central leaf. We conjecture that any Hecke-$\ell$-orbit is dense in the corresponding central leaf.
DOI : 10.1090/S0894-0347-04-00449-7

Oort, Frans  1

1 Mathematisch Instituut, Postbus 80.010, NL-3508 TA Utrecht, The Netherlands 
Oort, Frans. Foliations in moduli spaces of abelian varieties. Journal of the American Mathematical Society, Tome 17 (2004) no. 2, pp. 267-296. doi: 10.1090/S0894-0347-04-00449-7
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