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

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

2011-09-09

arxiv.org/abs/1109.2093v5

Mathematics

Number Theory

A "Concluding Remarks" Section added

Scientific paper

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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