The Z*-theorem for compact Lie groups.
Let be a differential (not necessarily commutative) algebra which carries a free action of a polynomial algebra with homogeneous generators . We show that for acyclic, the cohomology of the quotient
On construit un contre-exemple de la conjecture suivante : si la cohomologie modulo 2 réduite d'un polyGEM 1-connexe quelconque est de type fini et si elle n'est pas réduite à (0), alors elle contient au moins un élément non nilpotent.
We consider the cohomoly groups of compact locally Hermitian symmetric spaces with coefficients in the sheaf of germs of holomorphic sections of those vector bundles over the spaces which are defined by canonical automorphic factors. We give a quick survey of the research on these cohomology groups, and then discuss vanishing theorems of the cohomology groups.
An explicit basis of the space of global vector fields on the Sato Grassmannian is computed and the vanishing of the first cohomology group of the sheaf of derivations is shown.