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arXiv · 1205.6550

On base change of the fundamental group scheme

Axel Stäbler
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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.

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Axel Stäbler. 2012-05-30. On base change of the fundamental group scheme. https://arxiv.org/abs/1205.6550

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