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Mathematical Research Letters
Volume 19 (2012)
Number 2
On the Hasse principle for finite group schemes over global function fields
Pages: 453 – 460
DOI: https://dx.doi.org/10.4310/MRL.2012.v19.n2.a15
Authors
Abstract
Let $K$ be a global function field of characteristic $p>0$and let $M$ be a (commutative) finite and flat $K$-groupscheme. We show that the kernel of the canonicallocalization map $H^{1}\lbe(K,M)\longrightarrow\prod_{\e\text{all}\,\e v}\be H^{1}\lbe(K_{v},M)$ in flat(fppf) cohomology can be computed solely in terms of Galoiscohomology. We then give applications to the case where $M$is the kernel of multiplication by $p^{\le m}$ on anabelian variety defined over $K$.
Published 12 July 2012