Foliations in Moduli Spaces of Abelian Varieties and Dimension of Leaves

F. Oort

doi:10.1007/978-0-8176-4747-6_15

Foliations in Moduli Spaces of Abelian Varieties and Dimension of Leaves

F. Oort^*

^*Corresponding author for this work

Afd Mathematisch Instituut

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

In moduli spaces of abelian varieties and of p-divisible groups in characteristic p we have various foliations and statifications. 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.

Original language	English
Title of host publication	Algebra, arithmetic, and geometry : in honor of Yu. I. Manin
Editors	Yuri Tschinkel, Yuri Zarhin
Place of Publication	Boston [etc.]
Publisher	Birkhäuser
Pages	465-501
Number of pages	37
DOIs	https://doi.org/10.1007/978-0-8176-4747-6_15
Publication status	Published - 2010

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title = "Foliations in Moduli Spaces of Abelian Varieties and Dimension of Leaves",

abstract = "In moduli spaces of abelian varieties and of p-divisible groups in characteristic p we have various foliations and statifications. 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.",

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N2 - In moduli spaces of abelian varieties and of p-divisible groups in characteristic p we have various foliations and statifications. 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.

AB - In moduli spaces of abelian varieties and of p-divisible groups in characteristic p we have various foliations and statifications. 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.

U2 - 10.1007/978-0-8176-4747-6_15

DO - 10.1007/978-0-8176-4747-6_15

M3 - Conference contribution

SP - 465

EP - 501

BT - Algebra, arithmetic, and geometry : in honor of Yu. I. Manin

A2 - Tschinkel, Yuri

A2 - Zarhin, Yuri

PB - Birkhäuser

CY - Boston [etc.]

ER -

Foliations in Moduli Spaces of Abelian Varieties and Dimension of Leaves

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