TOTARO'S QUESTION ON ZERO-CYCLES ON TORSORS

摘要

Let G be a smooth connected linear algebraic group, and let X be a G-torsor. Totaro asked: If X admits a zero-cycle of degree d = 1, then does X have a closed etale point of degree dividing d? While the literature contains affirmative answers in some special cases, we give examples to show that the answer is negative in general.