p-adic Simpson Correspondence and Hodge-Tate Local Systems

Ahmed Abbes' research primarily focuses on the study of geometric and cohomological properties of sheaves on varieties over perfect fields of characteristic p>0 or p-adic fields, and their applications to arithmetic and algebraic geometry. He is the author/co-author of three books, including a seminal work on the p-adic Simpson Correspondence in collaboration with M. Gros and T. Tsuji.Michel Gros' research interests revolve around recent advancements in cohomology theories, both in characteristic p and in p-adic contexts. He has co-authored two books, including a seminal work on the p-adic Simpson Correspondence in collaboration with A. Abbes and T. Tsuji.

• Preface.- An overview.- Preliminaries.- Local Study.- Global Study.- Relative cohomologies of Higgs-Tate algebras.Local Study.- Relative cohomology of Dolbeault modules.- References.- Index..

“The Simpson correspondence ... establishes a correspondence between Higgs bundles and local systems on a compact Kähler manifold ... . The correspondence enjoys a number of  functoriality properties and it has found numerous applications in complex Hodge theory. ... Specifically, the present book studies two main themes: (1) Hodge-Tate local systems ... and (2) functoriality of the correspondence under proper higher direct images.” (Shishir Agrawal, zbMATH 1547.14002, 2024)