Logarithmic Riemann-Hilbert correspondences for rigid varieties.
By Hansheng Diao, Kai-Wen Lan, Ruochuan Liu, Xinwen Zhu. 2018
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On any smooth algebraic variety over a p-adic local field, we construct a tensor functor from the category of de Rham p-adic etale local systems to the category of filtered algebraic vector bundles with an integrable connection satisfying the Griffiths transversality, which we view as a p-adic analogue of Deligne's classical Riemann--Hilbert correspondence. The key intermediate step is to construct extensions of the desired connections to suitable compactifications of the algebraic variety with logarithmic poles along the boundary; hence the title of the paper. As an application, we show that this p-adic Riemann--Hilbert functor is compatible with the classical one over all Shimura varieties, for local systems attached to representations of the associated reductive algebraic groups.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c0241fc7bd578b657ff5cf4f12dea9316ca1b5e6
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- On locally analytic vectors of the completed cohomology of modular curves (2020, methodology): “eory of log adic spaces. See [DLLZ19, DLLZ18] for more details here. We will view Xas a log adic space by equipping it with the natural log structure defined by the cusps C:= X−Y, cf. Example 2.1.2 of [DLLZ18]. Then Vˆ defines a rank two Zˆ p-local system Vˆ log on Xprok´et, the pro-Kummer ´etale site”