On the Hasse principle for finite group schemes over global function fields
Number Theory
2012-01-18 v5 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.1109.2093,
title = {On the Hasse principle for finite group schemes over global function fields},
author = {Cristian D. Gonzalez-Aviles and Ki-Seng Tan},
journal= {arXiv preprint arXiv:1109.2093},
year = {2012}
}
Comments
A "Concluding Remarks" Section added