Trace of abelian varieties over function fields and the geometric Bogomolov conjecture
arXiv:1405.0896 · doi:10.1515/crelle-2015-0086
Abstract
We prove that the geometric Bogomolov conjecture for any abelian varieties is reduced to that for nowhere degenerate abelian varieties with trivial trace. In particular, the geometric Bogomolov conjecture holds for abelian varieties whose maximal nowhere degenerate abelian subvariety is isogenous to a constant abelian variety. To prove the results, we investigate closed subvarieties of abelian schemes over constant varieties, where constant varieties are varieties over a function field which can be defined over the constant field of the function field.
27 pages. An unnecessary assumption in Theorem 5.1 has been removed. Imprecise description of places has been corrected. To appear in Crelle. Different from the published version
References in corpus (3)
- The Bogomolov conjecture for totally degenerate abelian varieties
- Strict supports of canonical measures and applications to the geometric Bogomolov conjecture
- Geometric Bogomolov conjecture for abelian varieties and some results for those with some degeneration (with an appendix by Walter Gubler: The minimal dimension of a canonical measure)