Motivic torsors

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The torsor Pσ = Hom (HDR, Hσ) under the motivic Galois group Gσ = Aut Hσ of the Tannakian category Mk generated by one-motives related by absolute Hodge cycles over a field k with an embedding σ:k (rightwards arrow with hook) ℂ is shown to be determined by its projection Pσ → Pσ/G0σ to a Gal(k̄/k)- torsor, and by its localizations Pσk kξ at a dense subset of orderings ξ of the field k, provided k has virtual cohomological dimension (vcd) one. This result is an application of a recent local-global principle for connected linear algebraic groups over a field k of vcd ≤ 1.

Original languageEnglish
Pages (from-to)61-77
Number of pages17
JournalIsrael Journal of Mathematics
StatePublished - 2001
Externally publishedYes


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