On base change of the fundamental group scheme

2012/05/30 by Axel Stäbler, Stäbler, Axel
Mathematics · #14H30 #14H60 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1205.6550

openalex publication_date 2012/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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