Mathematische Zeitschrift

, Volume 277, Issue 1–2, pp 305–316 | Cite as

On base change of the fundamental group scheme

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Abstract

We provide for all prime numbers \(p\) examples of smooth projective curves over a field of characteristic \(p\) for which base change of the fundamental group scheme fails. This is intimately related to how \(F\)-trivial vector bundles, i.e. bundles trivialized by a power of the Frobenius morphism, behave in (trivial) families. We conclude with a study of the behavior of \(F\)-triviality in (not necessarily trivial) families.

Mathematics Subject Classification (1991)

Primary 14H30 14H60 
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Notes

Acknowledgments

This paper arose from discussions with Holger Brenner in relation to our joint paper [6]. In particular, I thank him for sparking my interest in this problem and for several useful discussions. Furthermore, I thank Manuel Blickle for useful discussions and the referee for a careful reading of an earlier draft and useful comments.

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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Johannes Gutenberg-Universität MainzMainzGermany

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