Zev Rosengarten
Published 2018-05-01Version 1
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 \v{C}esnavi\v{c}ius 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.
Counting points on $\text{Hilb}^m\mathbb{P}^2$ over function fields
Counting points of fixed degree and given height over function fields
On the distribution of the of Frobenius elements on elliptic curves over function fields
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