Duke Mathematical Journal

Totaro’s question on zero-cycles on torsors

R. Gordon-Sarney and V. Suresh

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1513998140

Digital Object Identifier
doi:10.1215/00127094-2017-0040

Mathematical Reviews number (MathSciNet)
MR3754631

Zentralblatt MATH identifier
1383.14003

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

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

Citation

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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