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.