scholarly journals On Selmer groups of abelian varieties over ℓ-adic Lie extensions of global function fields

2014 ◽  
Vol 45 (3) ◽  
pp. 575-595 ◽  
Author(s):  
Andrea Bandini ◽  
Maria Valentino
Keyword(s):  
Function Fields ◽  
Abelian Varieties ◽  
Selmer Groups ◽  
Global Function ◽  
Global Function Fields

scholarly journals Positivity of Hodge bundles of abelian varieties over some function fields

2021 ◽  
Vol 157 (9) ◽  
pp. 1964-2000
Author(s):  
Xinyi Yuan
Keyword(s):  
Finite Fields ◽  
Function Fields ◽  
Abelian Varieties ◽  
Global Function ◽  
Tate Conjecture ◽  
Global Function Fields

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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