Alterations and the prime-to-\(p\) fundamental group. (Altérations et groupe fondamental premier à \(p\)). (French) Zbl 1083.14506

Summary: Various results are proved relating to the largest quotient of the étale fundamental group prime to the residual characteristics, including the Künneth formula and invariance under change of separably closed field for schemes of finite type over a field. These are derived from general facts about direct images of stacks, once specialized to the case of torsors under a constant finite group of invertible order over the base. Analogous results for the tame fundamental group are discussed as well.


14F35 Homotopy theory and fundamental groups in algebraic geometry
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