Astérisque (448): Les suites spectrales de Hodge-Tate/ Ahmed Abbes & Michel Gros

Includes bibliography

La suite spectrale de Hodge-Tate relative – un survol -- Préliminaires -- Topos de Faltings -- Cohomologie du topos de Faltings -- Cohomologie relative des topos de Faltings -- Les suites spectrales de Hodge-Tate

This book presents two important results in p-adic Hodge theory following the approach initiated by Faltings, namely (i) his main p-adic comparison theorem, and (ii) the Hodge-Tate spectral sequence. We establish for each of these results two versions, an absolute one and a relative one. While the absolute statements can reasonably be considered as well understood, particularly after their extension to rigid varieties by Scholze, Faltings' initial approach for the relative variants has remained much less studied. Although we follow the same strategy as that used by Faltings to establish his main p-adic comparison theorem, part of our proofs is based on new results. The relative Hodge-Tate spectral sequence is new in this approach.