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日時: 2025年11月27日(木) 15:30-16:30
Date: November 27, 2025 15:30-16:30
会場:NISSAY Lecture Hall（大講義室）
Place: NISSAY Lecture Hall（auditorium）, Graduate School of Math. Sci. Bldg.
Ahmed Abbes 氏（IHES）
Ahmed Abbes (IHES)
The p-adic Simpson correspondence (ENGLISH)
The classical Simpson correspondence describes complex linear representations of the fundamental group of a smooth complex projective variety in terms of linear algebra objects, namely Higgs bundles. Inspired by this, Faltings initiated in 2005 a p-adic analogue, aiming to understand continuous p-adic representations of the geometric fundamental group of a smooth projective variety over a p-adic local field. Although the formulation mirrors the complex case, the methods in the p-adic setting are entirely different and build on ideas from Sen theory and Faltings’ approach to p-adic Hodge theory.
In this talk, I will survey the p-adic Simpson correspondence with a focus on the construction developed jointly with M. Gros, and on more recent work with M. Gros and T. Tsuji. In this latter work, we develop a new framework for studying the functoriality of the correspondence. The key idea is a novel twisting technique for Higgs modules using Higgs-Tate algebras, which is inspired by our earlier approach and encompasses it as a special case. The resulting framework provides twisted pullbacks and higher direct images of Higgs modules, allowing us to study the functoriality of the p-adic Simpson correspondence under arbitrary pullbacks and proper (log)smooth direct images by morphisms that do not necessarily lift to the infinitesimal deformations of the varieties chosen to construct the p-adic Simpson correspondence. Along the way, we clarify the relation of our framework with recent developments involving line bundles on the spectral variety.