Tate Duality in Positive Dimension over Function Fields

Concentrating mainly on the more difficult function field setting, we extend the classical duality results of Poitou and Tate for finite discrete Galois modules over local and global fields to all affine commutative group schemes of finite type, building on ?esnavi?ius' recent work extending these results to all finite commutative group schemes.

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We extend the classical duality results of Poitou and Tate for finite discrete Galois modules over local and global fields (local duality, nine-term exact sequence, etc.) to all affine commutative group schemes of finite type, building on the recent work of ?esnavi?ius [?es2] extending these results to all finite commutative group schemes. We concentrate mainly on the more difficult function field setting, giving some remarks about the number field case along the way.