Motivic torsors
Algebraic Geometry
2007-05-23 v1 Number Theory
Representation Theory
Abstract
The torsor P_s=Hom(H_{\DR},H_s) under the motivic Galois group G_s=Aut H_s of the Tannakian category M_k 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 [P_s\to (P_s)/(G_s)^0] to a Gal(\ov k/k)-torsor, and by its localizations (P_s) x_k (k_\xi) at a dense subset of orderings \xi 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.
Keywords
Cite
@article{arxiv.math/0003101,
title = {Motivic torsors},
author = {Yuval Z. Flicker},
journal= {arXiv preprint arXiv:math/0003101},
year = {2007}
}
Comments
12 pages, AMSTeX. Israel J. Math., accepted for publication