Manuel Blickle,
Poincare Lemma and Cartier Isomorphism for affine toric varieties
For smooth varieties over a field of characteristic zero (resp. finite
characteristic) the Poincare lemma (resp. the Cartier Isomorphism) gives a
complete description of the cohomology of the de Rham complex.
In this first meeting of the Student CAAG seminar in the new semester I
will give a painless introduction to the Cartier map and will explain why
it is relevant to mathematics.
Furthermore I will report on a proof of a Poincare type lemma for
affine toric varieties in characteristic zero due to Danilov and show how
his proof can be used to obtain the Cartier isomorphism in finite
characteristic in this case.