2018/03/15 by Diao, Hansheng, Lan, Kai-Wen, Liu, Ruochuan +1 · 2 citations
#14F30 #14G22 #14G35 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Primary 14F40 #Secondary 14D07
paper · doi:10.48550/arxiv.1803.05786
On any smooth algebraic variety over a p-adic local field, we construct a tensor functor from the category of de Rham p-adic étale local systems to the category of filtered algebraic vector bundles with integrable connections satisfying the Griffiths transversality, which we view as a p-adic analogue of Deligne's classical Riemann--Hilbert correspondence. A crucial step is to construct canonical extensions of the desired connections to suitable compactifications of the algebraic variety with logarithmic poles along the boundary, in a precise sense characterized by the eigenvalues of residues; 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.