La suite spectrale de Hodge-Tate

The Hodge-Tate spectral sequence for a proper smooth variety over a p-adic field provides a framework for us to revisit Faltings' approach to p-adic Hodge theory and to fill in many details. The spectral sequence is obtained from the Cartan-Leray spectral sequence for the canonical projection from the Faltings topos to the \'etale topos of an integral model of the variety. Its abutment is computed by Faltings' main comparison theorem from which derive all comparison theorems between p-adic \'etale cohomology and other p-adic cohomologies, and its initial term is related to the sheaf of differential forms by a construction reminiscent of the Cartier isomorphism.