Tate Duality in Positive Dimension over Function Fields 1KJW and even the uneven media

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Tate Duality in Positive Dimension over Function Fields 1KJW and even the uneven mediaWe 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