Franco-Asian Summer School on Arithmetic Geometry

Collection Franco-Asian Summer School on Arithmetic Geometry

Organizer(s) Ahmed Abbes (CNRS & IHÉS), Ana Caraiani (Imperial College London ), Ariane Mézard (Sorbonne Université), Takeshi Saito (University of Tokyo), Takeshi Tsuji (The University of Tokyo), Daxin Xu (Chinese Academy of Sciences), Weizhe Zheng (Chinese Academy of Sciences).
Date(s) 30/05/2022 - 03/06/2022
linked URL https://www.ihes.fr/~abbes/Luminy/luminy2022.html
00:00:00 / 00:00:00
22 23

Parallel transport for Higgs bundles over p-adic curves

By Daxin Xu

Faltings conjectured that under the p-adic Simpson correspondence, finite dimensional p-adic representations of the geometric étale fundamental group of a smooth proper p-adic curve X are equivalent to semi-stable Higgs bundles of degree zero over X. We will talk about an equivalence between these representations and Higgs bundles whose underlying vector bundle admits potentially a strongly semi-stable reduction of degree zero. These Higgs bundles are semi-stable of degree zero and we will investigate some evidence for Faltings' conjecture.

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