Stability of Arakelov bundles and tensor products without global sections

Details Stability of Arakelov bundles and tensor products without global sections Stability of Arakelov bundles and tensor products without global sections

2003-04-02

arxiv.org/abs/math/0304017v1

Documenta Math. 8 (2003), 115-123

Mathematics

Number Theory

8 pages

Scientific paper

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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