Positivity of Hodge bundles of abelian varieties over some function fields. (English) Zbl 1511.14039
Summary: 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.
MSC:
| 14G17 | Positive characteristic ground fields in algebraic geometry |
| 14G10 | Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) |
| 14G25 | Global ground fields in algebraic geometry |
| 14K15 | Arithmetic ground fields for abelian varieties |
Keywords:
Hodge bundle; ample vector bundle; function field; height; abelian scheme; Néron model; purely inseparable points; torsors; Tate-Shafarevich group; BSD conjecture; Tate conjectureReferences:
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