Compatibilité de la suite exacte de Poitou-Tate aux mesures de Haar
We study a deformation of the Kummer sequence to the radicial sequence over an -algebra, which is somewhat dual for the deformation of the Artin-Schreier sequence to the radicial sequence, studied by Saidi. We also discuss some relations between our sequences and the embedding of a finite flat commutative group scheme into a connected smooth affine commutative group schemes, constructed by Grothendieck.
We study the degree 3 cohomological invariants with coefficients in of a semisimple group over an arbitrary field. A list of all invariants of adjoint groups of inner type is given.
We give explicit formulas for reducing the problem of determining whether a given 2-cocycle is a coboundary and if so finding a lifting 1-cochain to a system of norm equations.