Tate Duality In Positive Dimension Over Function Fields

Zev Rosengarten

Tate Duality In Positive Dimension Over Function Fields

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arxiv 1805.00522 v9 pith:ZOWH6FIX submitted 2018-05-01 math.NT

Zev Rosengarten This is my paper · ORCID

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keywords dualityfinitecommutativefieldfieldsfunctiongrouplocal

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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 \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.

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F-isocrystals of Higher Direct Images of $p$-Divisible Groups
math.AG 2025-06 conditional novelty 7.0 of 10

For a p-divisible group G over a smooth projective X/k in characteristic p, the formal group R^i f_fppf* G is isogenous to a p-divisible group whose Dieudonné crystal is the slope-[0,1] part of R^i f_crys* M^cr(G).

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