On the \lq \lq Galois closure\rq \rq for torsors
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- 1 November 2009
- journal article
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 137 (11) , 3575
- https://doi.org/10.1090/s0002-9939-09-09997-3
Abstract
We show that a tower of torsors under affine group schemes can be dominated by a torsor. Moreover, if the base is the spectrum of a field and the structure group schemes are finite, the tower can be dominated by a finite torsor. As an application, we show that if X is a torsor under a finite group scheme G over a scheme S which has a fundamental group scheme, then X has a fundamental group scheme too and that this group π(X) identifies with the kernel of the map π(S) → GKeywords
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