Rendiconti del Seminario Matematico della Università di Padova


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Volume 128, 2012, pp. 55–89
DOI: 10.4171/RSMUP/128-4

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

Jean-Benoît Bost[1] and Gerard Freixas i Montplet[2]

(1) Université Paris-Sud, Orsay, France
(2) Institut de Mathématiques de Jussieu, Paris, France

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.

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Bost Jean-Benoît, Freixas i Montplet Gerard: Semi-Abelian Schemes and Heights of Cycles in Moduli Spaces of Abelian Varieties. Rend. Sem. Mat. Univ. Padova 128 (2012), 55-89. doi: 10.4171/RSMUP/128-4