Equivariant Stiefel-Whitney classes
This paper gives a number of results on equivariant Stiefel-Whitney classes for equivariant orthogonal vector bundles over schemes. If \(G\) is finite and acts trivially on the base \(X\), then \(H^i(X_{et},G;\mathbb{Z}/2)=\sum_{j+k=i}H^j(X_{et};\mathbb{Z}/2)\otimes H^k(G,\mathbb{Z}/2)\) so we may decompose the \(i\)th Stiefel-Whitney class into the sum of \(w_{j,k}\in H^j(X_{et};\mathbb{Z}/2)\otimes H^k(G,\mathbb{Z}/2)\). This paper investigates \(w_{1,1}\), calculates \(w_{j,k}\) for an illuminating example, and investigates Stiefel-Whitney classes of trace forms.
scientific article; zbMATH DE number 727072
scientific article