International Mathematics Research Notices

International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn050, 39 pages, doi:10.1093/imrn/rnn050 published on July 12, 2008

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© The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

Principal Bundles on p-Adic Curves and Parallel Transport

Urs Hackstein

Westfälische Wilhelms-Universität Münster, Mathematisches Institut, Einsteinstrasse 62, D-48149 Münster, Germany

Correspondence: Correspondence to be sent to: urs.hackstein{at}uni-ulm.de

We define functorial isomorphisms of parallel transport along étale paths for a class of principal G-bundles on a p-adic curve. Here G is a connected reductive algebraic group of finite presentation over the ring of integers of _p and the considered principal bundles are those with potential strongly semistable reduction of degree zero. The constructed isomorphisms yield continuous functors from the étale fundamental groupoid of the curve to the category of topological spaces with a simply transitive continuous right G(_p)-action. This generalizes a recent construction for vector bundles on a p-adic curve by Deninger and Werner. Our result can 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.

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Present address: Universität Ulm, Institut für Reine Mathematik, Helmholtzstrasse 18, D-89081 Ulm, Germany.

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This Article Abstract Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to My Personal Archive Download to citation manager Request Permissions How to cite this article Google Scholar Articles by Hackstein, U. Social Bookmarking          What's this?