Geodesic
Stability of Arakelov bundles and tensor products without global sections
Documenta mathematica, Tome 8 (2003), pp. 115-123
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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⊗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.
DOI : 10.4171/dm/141
Classification : 11H31, 11R56, 14G40
Mots-clés : tensor product, Arakelov bundle, arithmetic curve, lattice sphere packing, mean value formula, Minkowski-hlawka theorem 
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     author = {Norbert Hoffmann},
     title = {Stability of {Arakelov} bundles and tensor products without global sections},
     journal = {Documenta mathematica},
     pages = {115--123},
     year = {2003},
     volume = {8},
     doi = {10.4171/dm/141},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/141/}
}
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Norbert Hoffmann. Stability of Arakelov bundles and tensor products without global sections. Documenta mathematica, Tome 8 (2003), pp. 115-123. doi: 10.4171/dm/141

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