On the “Galois closure” for torsors
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- by Marco A. Garuti
- Proc. Amer. Math. Soc. 137 (2009), 3575-3583
- DOI: https://doi.org/10.1090/S0002-9939-09-09997-3
- Published electronically: June 25, 2009
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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 $\boldsymbol {\pi }(X)$ identifies with the kernel of the map $\boldsymbol {\pi }(S)\to G$.
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Bibliographic Information
- Marco A. Garuti
- Affiliation: Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova, Via Trieste 63, 35121, Padova, Italy
- Email: mgaruti@math.unipd.it
- Received by editor(s): February 14, 2008
- Received by editor(s) in revised form: October 29, 2008
- Published electronically: June 25, 2009
- Communicated by: Ted Chinburg
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 3575-3583
- MSC (2000): Primary 14L15, 14F20
- DOI: https://doi.org/10.1090/S0002-9939-09-09997-3
- MathSciNet review: 2529863