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On some Hasse principles for algebraic groups over global fields. (English) Zbl 1300.11032

Summary: We consider certain local-global principles related with some splitting problems for connected linear algebraic groups over global fields. The main tools are certain reciprocity results due to G. Prasad and A. S. Rapinchuk [Adv. Math. 207, No. 2, 646–660 (2006; Zbl 1132.20024)], G. Harder’s Hasse principle for homogeneous projective spaces of reductive groups for number fields [Jahresber. Dtsch. Math.-Ver. 70, 182–216 (1968; Zbl 0194.05701)] and their extensions to global function fields.

MSC:

11E72 Galois cohomology of linear algebraic groups
14F20 Étale and other Grothendieck topologies and (co)homologies
14L15 Group schemes
14G20 Local ground fields in algebraic geometry
20G10 Cohomology theory for linear algebraic groups
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References:

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