## Algebraic proofs of degenerations of Hodge-de Rham complexes

In the first half of the talk I shall present a new algebraic proof of a result of Deligne-Illusie about the degeneration of the Hodge-de Rham spectral sequence. The idea is to reduce the main technical point of their proof to a question about the formality of a derived intersection in an Azumaya space.