We give a sufficient condition for the injectivity of the global-to-local map of the relative Chow group of zero-cycles on a quadric fibration of dimension $\leq 3$ defined over a number field.
"Hasse Principle for the Chow Groups of Zero-cycles on Quadric Fibrations." Tokyo J. Math. 37 (2) 265 - 271, December 2014. https://doi.org/10.3836/tjm/1422452794