Positivity of Hodge bundles of abelian varieties over some function fields

Abstract

The main result of this paper concerns the positivity of the Hodge bundles of abelian varieties over global function fields. As applications, we obtain some partial results on the Tate--Shafarevich group and the Tate conjecture of surfaces over finite fields.

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Cited by in corpus (3)

• On the $\mu$-invariants of abelian varieties over function fields of positive characteristic
• Perfect points on genus one curves and consequences for supersingular K3 surfaces
• Comparison of different Tate conjectures