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arXiv · 1707.05049

On the trace forms of Galois algebras

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

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Philippe Cassou-Noguès, Ted Chinburg, Baptiste Morin, Martin J. Taylor. 2017-07-17. On the trace forms of Galois algebras. https://arxiv.org/abs/1707.05049

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