Ahmed Abbes, Mathematician
CNRS Research Director at IHES
Ahmed Abbes mainly studies geometrical and cohomological properties of sheaves on varieties on perfect fields of characteristic p>0 or on p-adic fields, designed for applications in arithmetic and algebraic geometry.
His joint work with Takeshi Saito led to a significant breakthrough in ramification theory. Ahmed Abbes is the author of a treatise presenting a systematic development of rigid geometry following Michel Raynaud’s approach, based on formal schemes up to admissible blow-ups.
His recent work focuses on the p-adic Hodge theory. He developed jointly with Michel Gros the p-adic Simpson correspondence initiated by Greg Faltings. It aims to describe all p-adic representations of the fundamental group of a smooth and proper variety over a p-adic field in terms of linear algebra – namely the Higgs bundles. Ahmed Abbes has published with Michel Gros and Takeshi Tsuji a book that undertakes a systematic development of the theory following two new approaches, one by him and Gros, the other by Tsuji.
More recently, Ahmed Abbes has established with Michel Gros the existence of a relative Hodge-Tate spectral sequence generalizing the Hodge-Tate decomposition of the p-adic étale cohomology of a smooth and proper variety over a p-adic field to a relative situation.
CNRS Bronze Medal (2005)
Distinguished Ordway visitor, the School of Mathematics of the University of Minnesota (2016)
