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

2011/09/09 by Cristian D. Gonzalez-Aviles, Cristian D. González-Avilés, Gonzalez-Aviles, Cristian D. +2 · 1 citation
Mathematics · #11G35 (Primary) 14K15 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #math.AG #math.NT #msc:11G35 #msc:14K15

paper · pdf · doi:10.48550/arxiv.1109.2093

A "Concluding Remarks" Section added

openalex publication_date 2011/09/09 · arxiv created 2012/01/17 · arxiv updated 2012/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 H¹(K,M)→∏_{all v}H¹(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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• Adelic Mordell-Lang and the Brauer-Manin obstruction

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