Mathematical Research Letters

Volume 19 (2012)

Number 2

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

Pages: 453 – 460



Cristian D. González-Avilés (Departamento de Matemáticas, Universidad de La Serena, Chile.)

Ki-Seng Tan (Department of Mathematics, National Taiwan University, Taipei 10764, Taiwan.)


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 $K$.

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