On the trace form of Galois algebras

International audienceWe study the trace form qL 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 qL. By combining this computation with work of Quillen we determine the isometry class of qL for large families of G-Galois algebras over global fields. We also indicate how our results generalize to Galois G-covers of schemes