- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:49
Rendiconti del Seminario Matematico della Università di Padova
Rend. Sem. Mat. Univ. Padova
RSMUP
0041-8994
2240-2926
General
10.4171/RSMUP
http://www.ems-ph.org/doi/10.4171/RSMUP
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2013)
128
2012
0
Semi-Abelian Schemes and Heights of Cycles in Moduli Spaces of Abelian Varieties
Jean-Benoît
Bost
Université Paris-Sud, ORSAY CEDEX, FRANCE
Gerard
Freixas i Montplet
C.N.R.S. - Institut de Mathématiques de Jussieu, PARIS CEDEX 05, 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.
General
55
89
10.4171/RSMUP/128-4
http://www.ems-ph.org/doi/10.4171/RSMUP/128-4