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arXiv · 1109.2093

On the Hasse principle for finite group schemes over global function fields

Cristian D. Gonzalez-Aviles·Ki-Seng Tan
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Abstract

Let K be a global function field of positive characteristic p and let M be a (commutative) finite and flat K-group scheme. We show that the kernel of the canonical localization map H^{1}(K,M)\to\prod_{all v}H^{1}(K_{v},M) in flat (fppf) cohomology can be computed solely in terms of Galois cohomology. We then give applications to the case where M is the kernel of multiplication by p^{m} on an abelian variety defined over K.

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Cristian D. Gonzalez-Aviles, Ki-Seng Tan. 2011-09-09. On the Hasse principle for finite group schemes over global function fields. https://arxiv.org/abs/1109.2093

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