【ハイブリッドによる開催】東工大数論・幾何学セミナー： Ahmed Abbes 氏

場所: 東京科学大学　大岡山キャンパス本館１階 M-110講義室（ハイブリッド開催）

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講演タイトル: Twisting Higgs modules and functoriality of the p-adic Simpson correspondence
要旨: 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. I will present a joint work with M. Gros and T. Tsuji, aimed at building a robust framework for a broader functoriality of the p-adic correspondence. We introduce a new method for twisting Higgs modules using Higgs-Tate algebras. This construction is inspired by our earlier joint approach with M. Gros to the p-adic Simpson correspondence, which it encompasses 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. In addition, we clarify how this new twisting relates to recent constructions involving line bundles on the spectral variety.

更新日：2026.04.07

【ハイブリッドによる開催】東工大 数論・幾何学セミナー： Ahmed Abbes 氏