Les suites spectrales de Hodge-Tate

Abstract

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.

411 page. in French language. Final version. The starting point of this work is our preprint arXiv:1509.03617 which is included in this monograph

Cited by in corpus (2)

• Cohomological Descent for Faltings' $p$-adic Hodge Theory and Applications
• Faltings extension and Hodge-Tate filtration for abelian varieties over $p$-adic local fields with imperfect residue fields