naa a22 4500 510782914 CHVBK 20180411083253.0 cr unu---uuuuu 180411e20130601xx s 000 0 eng 10.1007/s11856-012-0109-x doi (NATIONALLICENCE)springer-10.1007/s11856-012-0109-x Minima, pentes et algèbre tensorielle [Elektronische Daten] [Éric Gaudron, Gaël Rémond] Slopes of an adelic vector bundle exhibit a behaviour akin to successive minima. Comparisons between the two amount to a Siegel lemma. Here we use Zhang's version for absolute minima over the algebraic numbers. We prove a Minkowski-Hlawka theorem in this context. We also study the tensor product of two hermitian bundles bounding both its absolute minimum and maximal slope, thus improving an estimate of Chen. We further include similar inequalities for exterior and symmetric powers, in terms of some lcm of multinomial coefficients. Hebrew University Magnes Press, 2013 Gaudron Éric Institut Fourier, UMR 5582, Université Grenoble I, BP 74, 38402, Saint-Martin-d'Hères Cedex, France aut Rémond Gaël Institut Fourier, UMR 5582, Université Grenoble I, BP 74, 38402, Saint-Martin-d'Hères Cedex, France aut Israel Journal of Mathematics Springer US; http://www.springer-ny.com 195/2(2013-06-01), 565-591 0021-2172 195:2<565 2013 195 11856 https://doi.org/10.1007/s11856-012-0109-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0109-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gaudron Éric Institut Fourier, UMR 5582, Université Grenoble I, BP 74, 38402, Saint-Martin-d'Hères Cedex, France aut NATIONALLICENCE 700 1- Rémond Gaël Institut Fourier, UMR 5582, Université Grenoble I, BP 74, 38402, Saint-Martin-d'Hères Cedex, France aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 195/2(2013-06-01), 565-591 0021-2172 195:2<565 2013 195 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer