On the trace forms of Galois algebras

Philippe Cassou-Noguès; Ted Chinburg; Baptiste Morin; Martin J. Taylor

On the trace forms of Galois algebras

Number Theory 2017-07-18 v1

Authors: Philippe Cassou-Noguès , Ted Chinburg , Baptiste Morin , Martin J. Taylor

Abstract

We study the trace form $q_L$ of $G$ -Galois algebras $L/K$ when $G$ is a finite group and $K$ is a field of characteristic different from $2$ . We introduce in this paper the category of $2$ -reduced groups and, when $G$ is such a group, we use a formula of Serre to compute the second Hasse-Witt invariant of $q_L$ . By combining this computation with work of Quillen we determine the isometry class of $q_L$ for large families of $G$ -Galois algebras over global fields. We also indicate how our results generalize to Galois $G$ -covers of schemes.

Keywords

Galois algebras trace forms Hasse-Witt invariant Serre formula Quillen isometry class global fields Galois covers

Cite

@article{arxiv.1707.05049,
  title  = {On the trace forms of Galois algebras},
  author = {Philippe Cassou-Noguès and Ted Chinburg and Baptiste Morin and Martin J. Taylor},
  journal= {arXiv preprint arXiv:1707.05049},
  year   = {2017}
}

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17 pages

On the trace forms of Galois algebras

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Keywords

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