Criterion for surjectivity of localization in Galois cohomology of a reductive group over a number field

2022/09/05 by Borovoi, Mikhail, Rosengarten, Zev
#11E72 #20G10 #20G20 #20G25 #20G30 #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2209.02069

Abstract

Let G be a connected reductive group over a number field F, and let S be a set (finite or infinite) of places of F. We give a necessary and sufficient condition for the surjectivity of the localization map from H¹(F,G) to the "direct sum" of the sets H¹(F_v,G) where v runs over S. In the appendices, we give a new construction of the abelian Galois cohomology of a reductive group over a field of arbitrary characteristic.

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