Geodesic
Stability of Arakelov bundles and tensor products without global sections
Documenta mathematica, Tome 8 (2003), pp. 115-123.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 14G40, 11H31, 11R56
Keywords: Arakelov bundle, arithmetic curve, tensor product, lattice sphere packing, mean value formula, Minkowski-hlawka theorem 
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     title = {Stability of {Arakelov} bundles and tensor products without global sections},
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     url = {http://geodesic.mathdoc.fr/item/DOCMA_2003__8__a12/}
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Hoffmann, Norbert. Stability of Arakelov bundles and tensor products without global sections. Documenta mathematica, Tome 8 (2003), pp. 115-123. http://geodesic.mathdoc.fr/item/DOCMA_2003__8__a12/