© Chris Peus / IHES
Ahmed Abbes, Mathematician
CNRS Research Director at IHES
Ahmed Abbes primarily studies the geometric and cohomological properties of sheaves on varieties over perfect fields of characteristic p>0 or over p-adic fields, with a view towards applications in arithmetic and algebraic geometry.
His collaborative work with Takeshi Saito has led to significant breakthroughs in ramification theory. Ahmed Abbes is the author of a treatise that systematically develops rigid geometry following Michel Raynaud’s approach, based on formal schemes with admissible blowups.
In collaboration with Michel Gros and Takeshi Tsuji, Ahmed Abbes developed the p-adic Simpson correspondence initiated by Gerd Faltings. This correspondence aims to describe the p-adic representations of the fundamental group of an algebraic variety over a p-adic field in terms of Higgs bundles. He published a book with Michel Gros and Takeshi Tsuji that undertakes a systematic development of the theory following two new approaches: one he developed together with Michel Gros and the other by Takeshi Tsuji.
Together with Michel Gros, he established the existence of a relative Hodge-Tate spectral sequence, which generalizes the Hodge-Tate decomposition of the p-adic étale cohomology of a proper and smooth variety over a p-adic field to a relative setting. This work is documented in an Astérisque volume.
In a more recent book with Michel Gros, Ahmed Abbes established new features of the p-adic Simpson correspondence, inspired by their construction of the relative Hodge-Tate spectral sequence, notably the functoriality of this correspondence by proper direct image.
CNRS Bronze Medal (2005)
Distinguished Ordway visitor, the School of Mathematics of the University of Minnesota (2016)
