Motivic torsors
Yuval Z. Flicker
Abstract
The torsor Ps=Hom(H,Hs) under the motivic Galois group Gs=Aut Hs of the Tannakian category Mk generated by one-motives related by absolute Hodge cycles over a field k with an embedding s into the complex numbers is shown to be determined by its global projection [Ps (Ps)/(Gs)0] to a Gal( k/k)-torsor, and by its localizations (Ps) xk (kξ) at a dense subset of orderings ξof 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.
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