TY  - BOOK
AU  - Abbes,Ahmed
AU  - Gros,Michel
TI  - Astérisque (448): Les suites spectrales de Hodge-Tate
SN  - 9782856299883
U1  - 516.35 23
PY  - 2024///
CY  - Marseille
PB  - Société Mathématique de France
KW  - Algebraic Geometry
KW  - Number Theory
N1  - 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
N2  -      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.
ER  -