Lecture----数学院晨兴数学中心

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.
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