20 | IHES Annual Report 2020

Ahmed ABBES Mathematics, CNRS research director.

In 2020, AHMED ABBES published a book in collaboration with Michel Gros on Hodge-Tate spectral sequences which 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. They established two versions for each of these results, one absolute and one relative. Whereas absolute statements can reasonably be considered to be well understood, especially after their extension to rigid varieties by Scholze, there have been far fewer studies of Faltings' initial approach to relative variants. Although they followed the same strategy that

Faltings used to establish his main p-adic comparison theorem, some of their proofs are based on new results. The relative Hodge-Tate spectral sequence is novel in this approach.

SCIENTIFIC ACTIVITY

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DISTINCTIONS

CNRS Bronze Medal (2005) Distinguished Ordway visitor, the School of Mathematics of the University of Minnesota (April 2016)

Editor of: Astérisque (2010-2018) Tunisian Journal of Mathematics (Co-Managing Editor)

PUBLICATIONS

With M. Gros Les suites spectrales de Hodge Tate Book of 389 pages (2020), pre-publication arXiv:2003.04714.

The Relative Hodge Tate Spectral Sequence an Overview Pre-publication arXiv:2003.03790.

Ahmed Abbes at Takeshi Saito's mathematics seminar (January 2020)