Hasse principle for Rost motives
arXiv:1711.04356
Abstract
We prove a Hasse principle for binary direct summands of the Chow motive of a smooth projective quadric Q over a number field F. Besides, we show that such summands are twists of Rost motives. In the case when F has at most one real embedding we describe a complete motivic decomposition of Q.
17 pages, accepted to International Mathematics Research Notices