The p-adic Simpson Correspondence

By A. Abbes, Michel Gros, Takeshi Tsuji. 2016

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Semistable Higgs bundles, periodic Higgs bundles and representations of algebraic fundamental groups (2013, result): “In [6], Faltings has established an equivalence of categories between the category of generalized representations of the geometric fundamental group and the category of Higgs bundles over a p-adic curve, which has generalized the earlier work of DeningerWerner [2] on a partial p-adic analogue of Nar”
Rigidity and a Riemann–Hilbert correspondence for p-adic local systems (2016, methodology): “change to K. An etale morphism between anoid spaces is called standard etale if it is a 1It is pointed out by Abbes the subtlety to compare our construction with the construction of Abbes-Gros’ in [AGT], although we believe that they are essentially the same. 6 RUOCHUAN LIU AND XINWEN ZHU compositio”
Logarithmic Riemann-Hilbert correspondences for rigid varieties. (2018, methodology): “By reduction modulo t, we obtain the log p-adic Simpson functor Hlog, as first constructed by Faltings [Fal05] and Abbes–Gros–Tsuji [AGT16] in much greater generality.”
On locally analytic vectors of the completed cohomology of modular curves (2020, methodology): “. As an application, we will show that taking locally analytic vectors is exact under certain conditions. Results of this section are closely related to the work of Faltings [Fal05], Abbes-Gros-Tsuji [AGT16], Liu-Zhu [LZ17] on p-adic Simpson correspondences. See Remark 3.1.7 below. 3.1. Statement of”