Topology and purity for torsors

  • Benjamin Antieau

  • Ben Williams

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We study the homotopy theory of the classifying space of the complex projective linear groups to prove that purity fails for -torsors on regular noetherian schemes when is a prime. Extending our previous work when , we obtain a negative answer to a question of Colliot-Thélène and Sansuc, for all . We also give a new example of the failure of purity for the cohomological filtration on the Witt group, which is the first example of this kind of a variety over an algebraically closed field.

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Benjamin Antieau, Ben Williams, Topology and purity for torsors. Doc. Math. 20 (2015), pp. 333–355

DOI 10.4171/DM/492