Duke Mathematical Journal

Totaro’s question on zero-cycles on torsors

R. Gordon-Sarney and V. Suresh

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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 d1, then does X have a closed étale 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.

Article information

Duke Math. J., Volume 167, Number 2 (2018), 385-395.

Received: 7 February 2017
Revised: 13 July 2017
First available in Project Euclid: 23 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11E72: Galois cohomology of linear algebraic groups [See also 20G10]
Secondary: 20G25: Linear algebraic groups over local fields and their integers 20G39

zero-cycles torsors linear algebraic groups Galois cohomology division algebras splitting fields


Gordon-Sarney, R.; Suresh, V. Totaro’s question on zero-cycles on torsors. Duke Math. J. 167 (2018), no. 2, 385--395. doi:10.1215/00127094-2017-0040. https://projecteuclid.org/euclid.dmj/1513998140

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