Principal Bundles on p-Adic Curves and Parallel Transport

DOI10.1093/IMRN/RNN050zbMATH Open1201.14025arXiv0706.0925OpenAlexW2059263732MaRDI QIDQ3515927

Urs Hackstein

Publication date: 30 July 2008

Published in: IMRN. International Mathematics Research Notices (Search for Journal in Brave)

Abstract: We define functorial isomorphisms of parallel transport along 'etale paths for a class of principal $G$-bundles on a $p$-adic curve. Here $G$ is a connected reductive algebraic group of finite presentation and the considered principal bundles are just those with potentially strongly semistable reduction of degree zero. The constructed isomorphisms yield continous functors from the 'etale fundamental groupoid of the given curve to the category of topological spaces with a simply transitive continous right $G(mathbb{C}_p)$-action. This generalizes a construction in the case of vector bundles on a $p$-adic curve by Deninger and Werner. It may be viewed as a partial $p$-adic analogue of the classical theory by Ramanathan of principal bundles on compact Riemann surfaces, which generalizes the classical Narasimhan--Seshadri theory of vector bundles on compact Riemann surfaces.

Full work available at URL: https://arxiv.org/abs/0706.0925

zbMATH Keywords

parallel transport\(p\)-adic curvesétale paths

Mathematics Subject Classification ID

Arithmetic ground fields for curves (14H25) Curves over finite and local fields (11G20) Fibrations, degenerations in algebraic geometry (14D06) Coverings of curves, fundamental group (14H30) Vector bundles on curves and their moduli (14H60) Representation theory of groups (20C99)

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