2011/09/13 by Éric Gaudron, Gaudron, Éric, Gaël Rémond +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1109.2812
openalex publication_date 2011/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.