Exceptional loci on abelian varieties

The talk will be about a generalization of the Ueno locus for subvarieties of abelian varieties, the so-called anomalous locus, which naturally appears in the setting of unlikely intersections. In particular, the anomalous locus is known to be Zariski closed by Rémond. I will show that there is a generalized Ueno fibration. In the family setting, I will explain the Zariski closedness of fiber-wise anomalous locus in characteristic 0, and of fiber-wise Ueno locus in arbitrary characteristic.