Trace of abelian varieties over function fields and the geometric Bogomolov conjecture

開催日時
2014/12/19 金 10:30 - 12:00
場所
3号館152号室
講演者
山木 壱彦
講演者所属
京都大学数学教室
概要

Let us consider any closed subvariety of an abelian vareity over a function field.
The geometric Bogomolov conjecture insists that if it has dense small points,
then it should be a "special" subvariety. In our previous work, the conjecture
is reduced to the conjecture for nowhere degenerate abelian varieties.

In this talk, we show 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 obtain 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.