The classifying topos of a group scheme and invariants of symmetric bundles

Philippe Cassou-Noguès, Ted Chinburg, Baptiste Morin +1

Let $Y$ be a scheme in which 2 is invertible and let $V$ be a rank $n$ vector bundle on $Y$ endowed with a non-degenerate symmetric bilinear form $q$. The orthogonal group ${\bf O}…