Stability of Arakelov bundles and tensor products without global sections
Norbert Hoffmann
Mathematisches Institut Bunsenstraße 3-5 D-37073 Göttingen Germany
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Abstract
This paper deals with Arakelov vector bundles over an arithmetic curve, i.e. over the set of places of a number field. The main result is that for each semistable bundle E, there is a bundle F such that has at least a certain slope, but no global sections. It is motivated by an analogous theorem of Faltings for vector bundles over algebraic curves and contains the Minkowski-Hlawka theorem on sphere packings as a special case. The proof uses an adelic version of Siegel's mean value formula.
Cite this article
Norbert Hoffmann, Stability of Arakelov bundles and tensor products without global sections. Doc. Math. 8 (2003), pp. 115–123
DOI 10.4171/DM/141