Cartier isomorphism

In algebraic geometry, the Cartier isomorphism is a certain isomorphism between the cohomology sheaves of the de Rham complex of a smooth algebraic variety over a field of positive characteristic, and the sheaves of differential forms on the Frobenius twist of the variety. It is named after Pierre Cartier. Intuitively, it shows that de Rham cohomology in positive characteristic is a much larger object than one might expect. It plays an important role in the approach of Deligne and Illusie to the degeneration of the Hodge–de Rham spectral sequence.