Equivariant BSD conjecture over global function fields
アブストラクト
Under a certain finiteness assumption of Tate-Shafarevich groups, Kato and Trihan showed the BSD conjecture for abelian varieties over global function fields of positive characteristic. We explain how to generalise this to semi-stable abelian varieties“twisted by Artin character” over global function field(under some additional technical assumptions).
This is a joint work with David Burns and Mahesh Kakde. If time permits, I'd like to discuss further speculations for generalisations.