Geodesic
Topology and purity for torsors
Documenta mathematica, Tome 20 (2015), pp. 333-355
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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 PGLp​-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 PGLp​. 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. 
@article{10_4171_dm_492,
     author = {Benjamin Antieau and Ben Williams},
     title = {Topology and purity for torsors},
     journal = {Documenta mathematica},
     pages = {333--355},
     year = {2015},
     volume = {20},
     doi = {10.4171/dm/492},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/492/}
}
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Benjamin Antieau; Ben Williams. Topology and purity for torsors. Documenta mathematica, Tome 20 (2015), pp. 333-355. doi: 10.4171/dm/492

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