Vector bundles on p-adic curves and parallel transport

2004/03/30 by Christopher Deninger, Annette Werner, Deninger, Christopher +1 · 1 citation
Mathematics · #11G20 #14H30 #14H60 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories #math.AG #math.NT #msc:11G20 #msc:14H30 #msc:14H60

paper · pdf · doi:10.48550/arxiv.math/0403516

The main result is now valid for arbitrary reduction; Theorems 5, 16, 17, 18 and 20 are either improvements of results in the first version or new. The article will appear in Annales Sci. de l'ENS 56 pages

openalex publication_date 2004/03/30 · arxiv created 2005/04/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define functorial isomorphisms of parallel transport along etale paths for a class of vector bundles on a p-adic curve. All bundles of degree zero whose reduction is strongly semistable belong to this class. In particular, they give rise to representations of the algebraic fundamental group of the curve. This may be viewed as a partial analogue of the classical Narasimhan-Seshadri theory of vector bundles on compact Riemann surfaces.

Citations

• Vector Bundles Over an Elliptic Curve

Cited by

• A remark on the vanishing of Higgs fields in the p-adic Simpson correspondence

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