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Trace of abelian varieties over function fields and the geometric Bogomolov conjecture.
- Source :
- Journal für die Reine und Angewandte Mathematik; 2018, Vol. 2018 Issue 741, p133-159, 27p
- Publication Year :
- 2018
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00754102
- Volume :
- 2018
- Issue :
- 741
- Database :
- Complementary Index
- Journal :
- Journal für die Reine und Angewandte Mathematik
- Publication Type :
- Academic Journal
- Accession number :
- 131059865
- Full Text :
- https://doi.org/10.1515/crelle-2015-0086