DOCUMENTA MATHEMATICA, Vol. 20 (2015), 333-355

Benjamin Antieau and Ben Williams

Topology and Purity for Torsors

We study the homotopy theory of the classifying space of the complex projective linear groups to prove that purity fails for $\PGL_p$-torsors on regular noetherian schemes when $p$ is a prime. Extending our previous work when $p=2$, we obtain a negative answer to a question of Colliot-Thélène and Sansuc, for all $\PGL_p$. 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.

2010 Mathematics Subject Classification:

Keywords and Phrases:

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