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Stability of Arakelov bundles and tensor products without global sections

Norbert Hoffmann
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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 $E \otimes F$ 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.

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Norbert Hoffmann. 2003-04-02. Stability of Arakelov bundles and tensor products without global sections. https://arxiv.org/abs/math/0304017

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