Foliations in moduli spaces of abelian varieties and
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Foliations in moduli spaces of abelian varieties and dimension of leaves Frans Oort
Version 26-V-2005
Felix-Klein-Kolloquium, D¨ usseldorf, 2 July 2005 Informal notes; not for publication
Introduction In this talk I consider moduli spaces of polarized abelian varieties in characteristic p. Also we consider deformation spaces of p-divisible groups. In these spaces we describe foliations, as constructed in [25]. What are the dimensions of leaves in these foliations, see (2.8)? We compute the dimensions of the central leaves, both in the unpolarized case and in the polarized case. These computations use either a result on “minimal p-divisible groups”, see [29], plus a result by Wedhorn, see [32], or a construction basically due to Ching-Li Chai which gives a generalization of Serre-Tate coordinates, see [2]. The dimension of a leaf in the unpolarized case, ζ = N (X), see (8.3): (r (((# ( ( ( (( # r ((ν2 ( # # dim(CX (D)) = 0
