Parallel transport and the p-adic Simpson correspondence
arXiv:1601.00885 · doi:10.1017/fms.2017.7
Abstract
Deninger and Werner developed an analogue for p-adic curves of the classical correspondence of Narasimhan and Seshadri between stable bundles of degree zero and unitary representations of the topological fundamental group for a complex smooth proper curve. Using parallel transport, they associated functorially to every vector bundle on a p-adic curve whose reduction is strongly semi-stable of degree 0 a p-adic representation of the fundamental group of the curve. They asked several questions: whether their functor is fully faithful; whether the cohomology of the local systems produced by this functor admits a Hodge-Tate filtration; and whether their construction is compatible with the p-adic Simpson correspondence developed by Faltings. We answer these questions in this article.
81 pages, in French. arXiv admin note: substantial text overlap with arXiv:1509.03617, arXiv:1301.0904 by other authors