# On base change of the fundamental group scheme

Axel Stäbler

Number | 21 |
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Author | Axel Stäbler |

Year | 2012 |

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.