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Foliations in moduli spaces of abelian varieties and dimension of leaves. (English) Zbl 1247.14047

Tschinkel, Yuri (ed.) et al., Algebra, arithmetic, and geometry. In honor of Y. I. Manin on the occasion of his 70th birthday. Vol. II. Boston, MA: Birkhäuser (ISBN 978-0-8176-4746-9/hbk; 978-0-8176-4747-6/ebook). Progress in Mathematics 270, 465-501 (2009).
Summary: In moduli spaces of abelian varieties and of \(p\)-divisible groups in characteristic \(p\) we have various foliations and stratifications. In this paper we compute the dimensions of central leaves. We give three different proofs of these results, where every proof presents a different flavour of this beautiful topic. Components of Newton polygon strata for one fixed Newton polygon may have various different dimensions, according to properties of the polarizations considered; we show which dimensions do appear for a given Newton polygon. Hence dimensions of isogeny leaves can be computed this way.
For the entire collection see [Zbl 1185.00042].

MSC:

14L05 Formal groups, \(p\)-divisible groups
11G15 Complex multiplication and moduli of abelian varieties
14K10 Algebraic moduli of abelian varieties, classification
14L15 Group schemes
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