Title: Foliations in abelian schemes
Speaker: Prof. Ziyang Gao (CNRS and Princeton)
Time: 2017-8-18, 16:00-17:30
Place: S817
Abstract: Let $\mathcal{A}/S$ be an abelian scheme of relative dimension $g$ over a smooth quasi-projective complex variety. Suppose it has trivial isotrivial part. Restricted to a non-empty open simply-connected subset $\Delta$, there is a natural real-analytic isomorphism $i: \mathcal{A}|_{\Delta} \cong \Delta\times\mathbb{T}^{2g}$. We prove the following result: if an irreducible subvariety $\mathcal{X}$ of $\mathcal{A}$ satisfies $\mathcal{X}|_{\Delta} = i^{-1(\Delta \times Y)$ for some subset $Y \subset \mathbb{T}^{2g}$, then $\mathcal{X}$ is the translate of an abelian subscheme by a torsion section. The proof uses o-minimal theory.