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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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