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Galois module structure of some elementary p-abelian extensions

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Abstract

We determine the Galois module structure of the parameterizing space of elementary p-abelian extensions of a field K when Gal(K/F) is any finite p-group, under the assumption that the maximal pro-p quotient of the absolute Galois group of F is a free, finitely generated pro-p group, and that F contains a primitive pth root of unity if char(F) ≠ p.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California at Berkeley, 970 Evans Hall #3840, Berkeley, CA, 94720-3840, USA

    Lauren Heller

  2. Department of Mathematics, Western University, London, Ontario, N6A 5B7, Canada

    Ján Mináč & Tung T. Nguyen

  3. Department of Mathematics, Wellesley College, 106 Central Street, Wellesley, MA, 02481, USA

    Andrew Schultz

  4. School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Hai Ba Trung, Hanoi, Vietnam

    Nguyễn Duy Tân

Authors
  1. Lauren Heller
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  2. Ján Mináč
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  3. Tung T. Nguyen
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  4. Andrew Schultz
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  5. Nguyễn Duy Tân
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Corresponding author

Correspondence to Andrew Schultz.

Additional information

To Professor Moshe Jarden, with gratitude for his vision and encouragement

The second author is partially supported by the Natural Sciences and Engineering Research Council of Canada grant R0370A01. He also gratefully acknowledges the Faculty of Science Distinguished Research Professorship, Western Science, in years 2004/2005 and 2020/2021.

The second and third authors also gratefully acknowledge the support of Western Academy for Advanced Research at Western University.

The fourth author is partially supported by 2021 Wellesley College Faculty Awards.

The fifth author is funded by Vingroup Joint Stock Company and supported by Vingroup Innovation Foundation (VinIF) under the project code VINIF.2021.DA00030.

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Heller, L., Mináč, J., Nguyen, T.T. et al. Galois module structure of some elementary p-abelian extensions. Isr. J. Math. 257, 389–408 (2023). https://doi.org/10.1007/s11856-023-2540-6

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  • DOI: https://doi.org/10.1007/s11856-023-2540-6

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