Cohomological Invariants for $G$-Galois Algebras and Self-Dual Normal Bases

E. Bayer-Fluckiger; R. Parimala

doi:10.4171/dm/557

JournalsdmVol. 22pp. 1–24

Cohomological Invariants for $G$ -Galois Algebras and Self-Dual Normal Bases

E. Bayer-Fluckiger
Ecole Polytechnique Federale de Lausanne, EPFL/FSB/MATHGEOM/CSAG Station 8, 1015 Lausanne, Switzerland
R. Parimala
Department of Mathematics and Computer Science, Emory University Atlanta, GA 30322, USA

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Abstract

We define degree two cohomological invariants for $G$ -Galois algebras over fields of characteristic not 2, and use them to give necessary conditions for the existence of a self-dual normal basis. In some cases (for instance, when the field has cohomological dimension $\leq 2$ ) we show that these conditions are also sufficient.

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E. Bayer-Fluckiger, R. Parimala, Cohomological Invariants for $G$ -Galois Algebras and Self-Dual Normal Bases. Doc. Math. 22 (2017), pp. 1–24

DOI 10.4171/DM/557