Geodesic
Topology and purity for torsors
Documenta mathematica, Tome 20 (2015), pp. 333-355.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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. 
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     author = {Antieau, Benjamin and Williams, Ben},
     title = {Topology and purity for torsors},
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Antieau, Benjamin; Williams, Ben. Topology and purity for torsors. Documenta mathematica, Tome 20 (2015), pp. 333-355. http://geodesic.mathdoc.fr/item/DOCMA_2015__20__a32/