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Local-global Galois theory of arithmetic function fields

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Abstract

We study the relationship between the local and global Galois theory of function fields over a complete discretely valued field. We give necessary and sufficient conditions for local separable extensions to descend to global extensions, and for the local absolute Galois group to inject into the global absolute Galois group. As an application we obtain a local-global principle for the index of a variety over such a function field. In this context we also study algebraic versions of van Kampen′s theorem, describing the global absolute Galois group as a direct limit of local absolute Galois groups.

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Authors and Affiliations

  1. Department of Mathematics, University of Pennsylvania, Philadelphia, PA, 19104-6395, USA

    David Harbater & Julia Hartmann

  2. Department of Mathematics, Rutgers University, Piscataway, NJ, 08854-8019, USA

    Daniel Krashen

  3. Department of Mathematics and Computer Science, Emory University, Atlanta, GA, 30322, USA

    Raman Parimala & Venapally Suresh

Authors
  1. David Harbater
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  2. Julia Hartmann
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  3. Daniel Krashen
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  4. Raman Parimala
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  5. Venapally Suresh
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Correspondence to David Harbater.

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Harbater, D., Hartmann, J., Krashen, D. et al. Local-global Galois theory of arithmetic function fields. Isr. J. Math. 232, 849–882 (2019). https://doi.org/10.1007/s11856-019-1889-z

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  • DOI: https://doi.org/10.1007/s11856-019-1889-z

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