Let be a smooth connected linear algebraic group, and let be a -torsor. Totaro asked: If admits a zero-cycle of degree , then does have a closed étale point of degree dividing ? While the literature contains affirmative answers in some special cases, we give examples to show that the answer is negative in general.
R. Gordon-Sarney. V. Suresh. "Totaro’s question on zero-cycles on torsors." Duke Math. J. 167 (2) 385 - 395, 1 February 2018. https://doi.org/10.1215/00127094-2017-0040