JournalsrsmupVol. 128pp. 55–89

Semi-Abelian Schemes and Heights of Cycles in Moduli Spaces of Abelian Varieties

  • Jean-Benoît Bost

    Université Paris-Sud, Orsay, France
  • Gerard Freixas i Montplet

    Institut de Mathématiques de Jussieu, Paris, France
Semi-Abelian Schemes and Heights of Cycles in Moduli Spaces of Abelian Varieties cover
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Abstract

We study extension properties of Barsotti-Tate groups and we establish diophantine inequalities involving heights of cycles with respect to logarithmically singular hermitian line bundles on arithmetic varieties. We apply these results to bound heights of cycles on moduli spaces of abelian varieties, induced by quotients of abelian varieties by levels of Barsotti-Tate subgroups, over function fields over number fields. To achieve this aim, we combine our results with an effective version of Rumely's theorem on integral points on possibly open arithmetic surfaces and with Faltings' theorems on heights of abelian varieties in isogeny classes.

Cite this article

Jean-Benoît Bost, Gerard Freixas i Montplet, Semi-Abelian Schemes and Heights of Cycles in Moduli Spaces of Abelian Varieties. Rend. Sem. Mat. Univ. Padova 128 (2012), pp. 55–89

DOI 10.4171/RSMUP/128-4